SELECTED
PUBLICATIONS

Piotr Matus, Professor of Mathematics

Home Curriculum Vitae Publications

  1. Matus, P.P. and Rychagov, G.P. (1997) Mathematical modelling in biology and medicine: Reference book, Belaruskaya navuka, Minsk, 207 p. (in Russian).
  2. Самарский А.А., Вабищевич П.Н., Матус П.П.(1998) Разностные схемы с операторными множителями, Минск: Изд-во ЗАО “ЦОТЖ”, 1998, 442 с. (in Russian).
  3. Samarskii A.A., Matus, P.P., and Vabishchevich, P.N., (2002) Difference schemes with operator factors, Kluwer Academic Publishers, Boston/Dordrecht/London, 384 p.
  4. S. Lemeshevsky, P. Matus, D. Poliakov Exact finite-difference schemes. De Gruyter. – 2016, 243 p.

  1. P. P. Matus, B. D. Utebaev. Monotone difference schemes of higher accuracy for parabolic equations // Doklady of the National Academy of Sciences of Belarus, 2020, vol. 64, no. 4, pp. 391-398 (in Russian). https://doi.org/10.29235/1561-8323-2020-64-4-391-39
  2. P. P. Matus, H.T.K. Anh. Compact difference schemes for Klein-Gordon equa-tion // Doklady of the National Academy of Sciences of Belarus, 2020, vol. 64, no. 5, pp. 526-533 (in Russian). https://doi.org/10.29235/1561-8323-2020-64-5-526-533
  3. P. P. Matus, H.T.K. Anh. Compact difference schemes for Klein–Gordon equa-tion with variable coefficients // Doklady of the National Academy of Sciences of Belarus, 2021, vol. 65, no. 1, pp. 25-32 (in Russian). https://doi.org/10.29235/1561-8323-2021-65-1-25-3
  4. P. P. Matus P.P. and Utebaev B.D. Compact and monotone difference schemes for parabolic equations.// Mathem. Mod., 33(4), 60-78 (2021) (in Russian)
  5. Матус П.П., Х. Т. К. Ань. Компактные разностные схемы на трехточечном шаблоне для гиперболических уравнений второго порядка // Дифференц. уравнения. 2021, Т.57, №7, с.

  1. Matus, P.P. (2003) Stability of difference schemes for nonlinear time-dependent problems. Comput. Meth. Appl. Math., 3(2): 313-329.
  2. Matus, P. and Martsynkevich, G. (2005) On the stability of a monotone difference scheme for the Burgers equation. Differents. Uravneniya, 41(7): 955-960. (in Russian); transl. in Differential Equations, 41(7): 1003-1009.
  3. Matus, P., Koroleva, O., Chuiko, M. (2007) Stability of difference schemes for equations of weakly compressible liquid. Comput. Meth. Appl. Math., 7(3): 208-220.
  4. Matus, P. and Kolodynska, A.(2008) Nonlinear stability of the difference schemes for equations of isentropic gas dynamics. Comput. Meth. Appl. Math., 8(2): 155-170.
  5. Matus, P.P. and Chuiko, M.M. (2009) Investigation of the stability and convergence of difference schemes for a polytropic gas with subsonic flows Differ. Equ. 45, No. 7, 1074-1085 (in English); translation from Differ. Uravn. 45, No. 7, 1053-1064 (2009).
  6. Matus P., and Lemeshevsky S.V. (2009) Stability and monotonicity of difference schemes for nonlinear scalar conservation laws and multidimensional quasi-linear parabolic equations Comput. Method Appl. Math. 9(3): 253 - 280.
  7. Marcinkiewicz, G.L., Matus, P.P., and Chuiko, M.M. (2010) Stability of difference schemes in terms of Riemann invariants for a polytropic gas Zh. Vychisl. Mat. Mat. Fiz. 50, No. 6, 1078-1091 (in Russian); translation in Comput. Math., Math. Phys. 50, No. 6, 1024 5 1037 (2010).
  8. Matus, P.P. (2010) Stability with respect to the initial data and monotonicity of an implicit difference scheme for a homogeneous porous medium equation with a quadratic nonlinearity Differ. Equ. 46, No. 7, 1019-1029 (in English); translation from Differ. Uravn. 46, No. 7, 1011-1021 (2010).
  9. Matus P., Polyakov D. (2012) Stability and convergence of the difference schemes for equations of isentropic gas dynamics in Lagrangian coordinates. Publ. Inst. Math. 91 (105):137-153.
  10. Jovanovic B., Lapinska-Chrzczonowicz M., Matus A., Matus P. (2012) Stability of finite-difference schemes for IBVP for multidimensional parabolic equations with a nonlinear source of the power type. Comp. Meth. Appl. Math. 12(3):289-305.
  11. P.P. Matus, I.N. Panayotova, D.B. Polyakov (2012) Stability and Monotonicity of a Conservative Difference Scheme for a Multidimensional Nonlinear Scalar Conservation Law. Differential Equations. 48(7):982–989.
  12. Matus, P.P. (2013) On the role of conservation laws in the problem of occurrence of unstable solutions for quasi-linear parabolic equations and their approximations Differ. Equ. 49, No. 7 (in English); translation from Differ. Uravn. 49, No. 7 (2013).

  1. S. Lemeshevsky, P. Matus, D. Poliakov Exact finite-difference schemes. De Gruyter. – 2016, 243 p.
  2. Matus, P.P., Irkhin, U. and Lapinska-Chrzczonowicz, M. (2005) Exact difference schemes for time-dependent problems. Comput. Meth. Appl. Math., 5(4): 422-448.
  3. Matus, P.P., Irkhin, U., Lapinska-Chrzczonowicz, M. and Lemeshevsky S.V.(2006) About exact difference schemes for hyperbolic and parabolic equations. Differ. Uravn. 43(7): 978-986 (In Russian).
  4. Kruk, A., Matus, P.(2007) High accuracy difference schemes for nonlinear transfer equation. Exact difference schemes for time-dependent problems. Math. Model. Anal. 12(4): 469-482.
  5. Matus, P., Kolodynska, A. (2007) Exact difference schemes for hyperbolic equations. Comput. Meth. Appl. Math., 7(4): 341-364.
  6. Laspinska-Chrzczonowicz, M., Matus, P.(2008) Exact difference schemes for hyperbolic equations. Int. J. Numer. Anal. Mod. 5(2): 303-319.
  7. Matus P.P., Kirshtein A.A., Irknin V.A. (2011) Exact difference schemes for the system of acoustic equations and analysis of Riemann problem. J. Numer.  Appl. Math. 2(105):83-97. 
  8. Lapinska-Chrzczonowicz, M., Matus, P. (2013). Exact difference schemes and schemes of higher order of approximation for convection-diffusion equation. I. Annales UMCS, Informatica. 3(1):37-51.
  9. Matus, P., Poliakov, D. (2013).Exact finite difference schemes for three-dimensional advection-reaction equations. Journal of Coupled Systems and Multiscale Dynamics. 1(4):428-433
  10. Lapinska-Chrzczonowicz, M., Matus, P. (2014).Exact difference schemes for a two-dimensional convection–diffusion–reaction equation.Computers & Mathematics with Applications. Computers & Mathematics with Applications. 67(12):2205–2217.
  11. Matus P., Poliakov D. Exact L1-conservative finite-difference scheme for the Neumann problem for heat conduction equation. // Applied mathematics, infor-matics and mechanics. – 2016. – Vol. 21. – No. 1. – P.33 – 43.
  12. Matus P., Poliakov D. Exact L1-conservative finite-difference scheme for the Neumann problem for quasilinear parabolic equation. // Recent Developments in Mathematics and Informatics, Contemporary Mathematics and Computer Sci-ence. –Vol. 1. – Ed. A. Zapała, Wydawnictwo KUL. – Lublin. – 2016. – Ch. 12. –P. 155 –166

  1. Samarskii, A.A., Vabishchevich, P.N., and Matus, P.P. (1997) The strong stability of differential-operator and operator-difference schemes. Dokl. Ross. Akad. Nauk, 356(4): 455-457. (in Russian); transl. in Dokl. Math., 56(2): 726-728.
  2. Matus, P.P. and Panaiotova, I.N. (1999) Strong stability of operator-differential equations and operator-difference schemes. Differents. Uravneniya, 35(2): 256-265. (in Russian); transl. in Differential Equations, 35(2): 257-268.
  3. Matus, P.P. and Jovanovich, B.S. (1999) Coefficient stability of operator-difference schemes. Mathematical Modeling and Analysis (MMA), 4: 135-146.
  4. Samarskii, A.A., Gulin A.V., and Matus P.P. (2000) Sufficient conditions of the coefficient stability of operator-difference schemes. Dokl. Ross. Akad. Nauk, 373(3): 304 - 306.
  5. Jovanovich, B.S. and Matus, P.P. (2001) Strong stability of operator-differential equations and operator-difference schemes in norms integral with respect to time. Differents. Uravneniya, 37(7): 950-958. (in Russian); transl. in Differential Equations, 37(7): 998-1008.
  6. Matus P.P. and Panaiotova, I.N. (2001) Coefficient stability of three-layer operator-difference schemes. Zh. Vychisl. Mat. Mat. Fiz. 41(5): 722-731.
  7. Samarskii A.A., Matus, P.P., and Vabishchevich, P.N., (2002) Difference schemes with operator factors, Kluwer Academic Publishers, Boston/Dordrecht/London, 384 p.
  8. Matus, P.P. (2002) The maximum principle and some of its applications. Comp. Meth. Appl. Math., 2(1): 50-91.
  9. Jovanovich, B.S. and Matus, P.P. (2002) Coefficient stability of differential-operator equations of the second order.. Differents. Uravneniya, 38(10): 1371-1377.
  10. Bojovich, D.R., Jovanovich, B.S. and Matus, P.P. (2004) On the strong stability of first-order operator-differential equations. Differents. Uravneniya, 40(5): 655-661. (in Russian); transl. in Differential Equations, 40(5): 703-710.
  11. Lemeshevskii, S.V., Matus, P.P. and Naumovich, A.R. (2004) A criterion for coefficient stability. Differents. Uravneniya, 40(7): 978-984. (in Russian); transl. in Differential Equations, 40(7): 1043-1050.
  12. Jovanovich, B., Lemeshevsky, B., Matus, P. and Vabishchevich, P.N. (2006) Stability of solutions of differential-operator and operator-difference equations in the sense of perturbation of operators. Comp. Meth. Appl. Math., 6(3): 269-290.
  13. Jovanovich, B., Matus, P. (2007) Strong stability of operator-difference equations. Int. J. Appl. Math. and Statistics, 10(507): 978-984;
  14. P. P.Matus, S.V. Lemeshevsky Coefficient stability of the solution of the finite-difference scheme approximating the initial boundary value problem for semi-linear parabolic equation. // Differential Equations, 2018, Vol 54, No. 7, pp. 929–937.
  15. Matus P. P., Lemeshevsky S. V. Stability with respect to coefficients of solutions of difference schemes approximating initial boundary-value problems for semi-linear hyperbolic equations // Doklady of the National Academy of Sciences of Belarus, 2020, vol. 64, no. 2, pp. 135–143 (in Russian). https://doi. org/10.29235/1561-8323-2020-64-2-135-14
  16. P. P.Matus, S.V. Lemeshevsky Stability of Solutions of Second-Order Differen-tial-Operator Equations and of Their Difference Approximations. // Differential Equations, 2020, Vol 56, No. 7, pp. 923–934

Hydraulic systems
  1. Koldoba, A.V., Poveshchenko, J.A., Matus, P.P., and Chuiko, M.M. (1992) Mathematical modeling of liquid flow in ramified hydraulic systems. Mathematical Modeling, 4(9): 43-54. (in Russian).
Microelectronics
  1. Ananich, S.E, Matus, P.P., and Mozolevski, I.E. (1997) Difference schemes for Bolzmann-Fokker-Planck equation. Mathematical Modeling, 9(1): 99-115. (in Russian).
  2. Komarov, F.F., Mozolevski, I.E., Matus, P.P., and Ananich, S.E. (1997) Distribution of implanted impurities and deposited energy in high-energy ion implantation. Journal of Technical Physics, 67(1): 61-67.
  3. Komarov,F.F., Mozolevski, I.E., Matus, P.P., and Ananich, S.E. (1997) Distribution of implanted impurities and deposited energy in high-energy ion implantation. Nucl. Instr. and Meth. B 97 (124): 478-483.
Biology and Medicine
  1. Matus, P.P. and Rychagov, G.P. (1997) Mathematical modelling in biology and medicine: Reference book, Belaruskaya navuka, Minsk, 207 p.. (in Russian).
Nonlinear Thermoelasticity: Modelling Matherials with Shape Memory
  1. Melnik, R.V.N., Wang, L., Matus, P. and Rybak, I. (2003) Computational aspects of conservative difference schemes for shape memory alloys applications, Lecture Notes in Computer Science, 2668, 791-800.
  2. Matus, P., Melnik, R.V.N., Wang, L., and Rybak, I. (2004) Nonlinear thermoelasticity: modelling matherials with shape memory Mathematics and Computers in Simulation, 65, 489-509.
Numerical methods for a non-linear Biot's model
  1. Matus P. P., Tuyen Vo Thi Kim, Gaspar F. Monotone difference schemes for lin-ear parabolic equations with mixed boundary conditions // Doklady of the Na-tional academy of science of Belarus. – 2014. – V. 58, No. 5, P. 18–22.
  2. F.J. Gaspar, F.J. Lisbona, P. Matus, V.T.K. Tuyen Numerical methods for a one-dimensional non-linear Biot’s model // Journal of Computational and Ap-plied Mathematics. –2016. – V. 293, February 2016, P. 62 –72
  3. F.J. Gaspar, F.J. Lisbona, P. Matus, V.T.K. Tuyen Monotone finite difference schemes for quasilinear parabolic problems with mixed boundary conditions // Comp. Meth. Appl. Math. –2016. – Vol. 16. – No. 2. –P. 231-243.

  1. Ananich, C.E, Matus, P.P. and Mozolevski, I.E. (1997) Difference schemes for Bolzmann-Fokker-Planck equation.. Mathematical Modeling, 9(1): 99-115.
  2. Samarskii, A.A., Matus, P.P., and Rychagov, V.G. (1997) Monotone difference schemes of high order on nonuniform grids. Mathematical Modeling, 9(2): 95-96. (in Russian).
  3. Samarskii, A.A., Vabishchevich, P.N., and Matus, P.P. (1997) Stability of vector additive schemes. Dokl. Ross. Akad. Nauk, 361(6): 746-748. (in Russian); transl. in Dokl. Math., 58(1): 133-135.
  4. Matus, A.P. and Matus, P.P. (2001) The maximum principle and its application for the investigation of stability and convergence of difference schemes. Mathematical Modeling and Analysis (MMA), 6(2): 289-299.
  5. Matus, P.P. (2002) The maximum principle and some of its applications. Comp. Meth. Appl. Math., 2(1): 50-91.
  6. Matus, P.P. and Rybak, I.V. Monotone difference schemes for nonlinear parabolic equations Differents. Uravneniya, 39(7): 960-968. (in Russian); transl. in Differential Equations, 39(7): 1013-1022.
  7. Matus, P. and Martsynkevich, G. (2004) Monotone and economical difference schemes on non-uniform grids for multidimensional parabolic equations with boundary conditions of the third kind. Comp. Meth. Appl. Math, 4(3): 350-367
  8. Matus, P. and Rybak, I. (2004) Difference schemes for elliptic equations with mixed derivatives. Comp. Meth. Appl. Math, 4(4): 494-505
  9. P.P. Matus, I.N. Panayotova, D.B. Polyakov (2012) Stability and Monotonicity of a Conservative Difference Scheme for a Multidimensional Nonlinear Scalar Conservation Law. Differential Equations. 48(7):982–989.
  10. Матус П.П., Утебаев Б.Д. Монотонные схемы произвольного порядка точности для уравнения переноса // Ж. вычисл. матем. и матем. физ. 2021.Т.61. №
  11. Matus P.P., Pylak D., Hieu L.M. Monotone Finite-Difference Schemes of Sec-ond-Order Accuracy for Quasilinear Parabolic Equations with Mixed Deriva-tives // Differential Equations, 2019, Vol 55, No. 3, pp. 424-436
  12. P. Matus, F.J. Gaspar, L.M. Hieu, V.T.K. Tuyen Monotone difference schemes for weakly coupled elliptic and parabolic systems // Comp. Meth. Appl. Math. –2017. – Vol. 17. – No. 2. – P. 287 – 298
  13. Ф.Ж. Гаспар, П.П. Матус, В.Т.К. Туен, Л.М. Хиеу Монотонные разност-ные схемы для систем эллиптических и параболических уравнений// Докла-ды НАН Беларуси. – 2016. – Т. 60, № 5. – С. 29–33
  14. F.J. Gaspar, F.J. Lisbona, P. Matus, V.T.K. Tuyen Monotone finite difference schemes for quasilinear parabolic problems with mixed boundary conditions // Comp. Meth. Appl. Math. –2016. – Vol. 16. – No. 2. –P. 231-243

  1. Vabishchevich, P.N., Matus, P.P., and Shcheglik, V.S. (1994) Operator-difference equations of divergent type. Differents. Uravneniya, 30(7): 1175-1186. (in Russian); transl. in Differential Equations, 30(7): 1088-1100.
  2. Samarskii, A.A., Matus, P.P., and Vabishchevich, P.N. (1998) Stability and convergence of two-level difference schemes in integral with respect to time norms. M3AS: Mathematical Models and Methods in Applied Sciences, 8(6): 1055-1070.
  3. Samarskii, A.A., Vabishchevich, P.N., and Matus, P.P. (1998) Stability of vector additive schemes. Dokl. Ross. Akad. Nauk, 361(6): 746-748. (in Russian); transl. in Dokl. Math., 58(1): 133-135.
  4. Korzyuk, V.I., Lemeshevsky, S.V., and Matus, P.P. (1999) Conjugation problem about jointly separate flow of viscoelastic and viscous fluids in the plane duct. Math. Model. and Analys. (MMA), 4: 114-123.
  5. Mazhukin, V.I., Matus, P.P., and Mikhailyuk, I.A. (2000) Finite-difference schemes for the Korteweg-de Vries equation. Differents. Uravneniya, 36(5): 709-716. (in Russian); transl. in Differential Equations, 36(5): 789-797.
  6. Jovanovich, B.S. and Matus, P.P. (2001) Strong stability of operator-differential equations and operator-difference schemes in norms integral with respect to time. Differents. Uravneniya, 37(7): 950-958. (in Russian); transl. in Differential Equations, 37(7): 998-1008.
  7. Matus, P.P. and Zjuzina, E.L. (2001) Three-level difference schemes on non-uniform in time grids. Comput. Meth. Appl. Math., 1(3): 265-284.
  8. Samarskii A.A., Matus, P.P., and Vabishchevich, P.N., (2002) Difference schemes with operator factors, Kluwer Academic Publishers, Boston/Dordrecht/London, 384 p.
  9. Jovanovich, B., Lemeshevsky, B., and Matus, P. (2002) On the stability of differential-operator equations and operator-difference schemes Comp. Meth. Appl. Math., 2(2): 153-170.
  10. Jovanovich, B.S. and Matus, P.P. (2003) Asymptotic Stability of First- and Second-Order Operator-Differential Equations Differents. Uravneniya, 39(3): 383-392. (in Russian); transl. in Differential Equations, 39(3): 414-425.
  11. Bojovich, D.R., Jovanovich, B.S. and Matus, P.P. (2004) On the strong stability of first-order operator-differential equations. Differents. Uravneniya, 40(5): 655-661. (in Russian); transl. in Differential Equations, 40(5): 703-710.
  12. Lemeshevskii, S.V., Matus, P.P. and Naumovich, A.R. (2004) A criterion for coefficient stability. Differents. Uravneniya, 40(7): 978-984. (in Russian); transl. in Differential Equations, 40(7): 1043-1050.
  13. Jovanovich, B., Lemeshevsky, B., Matus, P. and Vabishchevich, P.N. (2006) Stability of solutions of differential-operator and operator-difference equations in the sense of perturbation of operators. Comp. Meth. Appl. Math., 6(3): 269-290.
  14. Jovanovich, B. and Matus, P. (2007) Strong stability of operator-difference equations Int. J. Appl. Math. and Statistics., 10(507): 50-69.
  15. П. П. Матус, Ле Минь Хиеу, Д. Пылак, Разностные схемы для квазили-нейных параболических уравнений со смешанными производными // Докла-ды НАН Беларуси, 2019. Т. 63, № 3, c. 263-269

  1. Abrashin, V.N. and Matus, P.P. (1978) Difference methods for nonlinear hyperbolic equations with piecewise-smooth solutions. Differents. Uravneniya, 14(12): 2223-2240. (in Russian); transl. in Differential Equations, 14(12): 1576-1589.
  2. Abrashin, V.N. and Matus, P.P. (1979) Difference methods for nonlinear hyperbolic equations with piecewise-smooth solutions. II. Differents. Uravneniya, 15(7): 1225-1239. (in Russian); transl. in Differential Equations, 15(7): 870-881.
  3. Matus, P.P. (1980) On convergence of difference schemes for one-dimensional gasdynamics. PhD thesis, Minsk: 124 p.. (in Russian).
  4. Abrashin, V.N. and Matus, P.P. (1981) Accuracy of finite-difference schemes for one-dimensional gasdynamics. Differents. Uravneniya, 17(7): 1155-1170. (in Russian); transl. in Differential Equations, 17(7): 731-744.
  5. Matus, P.P. and Shavel', A.N. (1984) Convergence of finite-difference schemes for one-dimensional gasdynamics problems with thermal conductivity. Differents. Uravneniya, 19(7): 1251-1261. (in Russian); transl. in Differential Equations, 19(7): 932-941.
  6. Matus, P.P. (1985) Unconditional convergence of some finite-difference schemes for gasdynamics problems. Differents. Uravneniya, 21(7): 1227-1238. (in Russian); transl. in Differential Equations, 21(7): 839-848.
  7. Matus, P.P. and Stanishevskaya, L.I. (1991) Uncondotional convergence of difference schemes for nonstationary quasilinear equations of mathematical physics. Differents. Uravneniya, 27(7): 1203-1219. (in Russian); transl. in Differential Equations, 27(11): 847-859.
  8. Vabishchevich, P.N., Matus, P.P., and Rychagov, V.G. (1995) A class of difference schemes on dynamic locally concentrating grids. Differents. Uravneniya, 31(5): 849-857. (in Russian); transl. in Differential Equations, 31(5): 787-796.
  9. Matus, P.P., Moskal'kov, M.N., and Tscheglik, V.S. (1995) Consistent estimates of the convergence rate for the grid method in the case of a second-order nonlinear equation with generalized solutions. Differents. Uravneniya, 31(7): 1219-1226. (in Russian); transl. in Differential Equations, 31(7): 1198-1207.
  10. Jovanovich, B.S., Matus, P.P., and Tscheglik, V.S. (1999) On accuracy of difference schemes for nonlinear parabolic equations with generalized solutions. Zh. Vychisl. Mat. Mat. Fiz., 39(10): 1679-1686. (in Russian); transl. in Comp. Math. Math. Phys., 39(10): 1611-1618.
  11. Jovanovich, B.S., Matus, P.P., and Tscheglik, V.S. (2000) The estimates of accuracy of difference schemes for the nonlinear heat equation with weak solutions. Mathematical Modeling and Analysis (MMA), 5: 86-96.
  12. Matus P. (2014) On convergence of difference schemes for IBVP for quasilinear parabolic equations with generalized solutions. Comp. Meth. Appl. Math. 14(3):361 - 371.
  13. P. Matus, D. Poliakov, L. M. Hieu, On convergence of difference schemes for Dirichlet IBVP for two-dimensional quasilinear parabolic equations with mixed derivatives and generalized solutions // Comput. Methods in Appl. Math. 20 (2020), № 4.
  14. Piotr Matus, Dmitriy Poliakov, Dorota Pylak, On convergence of difference schemes for Dirichlet IBVP for two-dimensional quasilinear parabolic equa-tions, International Journal of Environment and Pollution, 2019, Vol 66, pp. 63-79.
  15. Piotr Matus, Dmitriy Poliakov, Le Minh Hieu On the consistent two-side esti-mates for the solutions of quasilinear convection-diffusion equations and their approximations on non-uniform grids // Journal of Computational and Applied Mathematics, 2018, Vol. 340, pp. 571-581
  16. Matus, P. P., Poliakov, D. B. Consistent two-sided estimates for the solutions of quasilinear parabolic equations and their approximations. // Differential Equa-tions, 2017, Vol 53, No. 7, pp. 964-973.

  1. Samarskii, A.A., Mazhukin, V.I., and Matus, P.P. (1997) $L_2$-conservative schemes for the Korteweg-de Vries equation. Dokl. Ross. Akad. Nauk, 357(4): 458-461. (in Russian); transl. in Dokl. Math., 56(3): 909-912.
  2. Mazhukin, V.I., Matus, P.P., and Mikhailyuk, I.A. (2000) Finite-difference schemes for the Korteweg-de Vries equation. Differents. Uravneniya, 36(5): 709-716. (in Russian); transl. in Differential Equations, 36(5): 789-797.
  3. Samarskii A.A., Matus, P.P., and Vabishchevich, P.N., (2002) Difference schemes with operator factors, Kluwer Academic Publishers, Boston/Dordrecht/London, 384 p.
  1. Vabishchevich, P.N., Lemeshevskij, S.V., and Matus, P.P. (1998) Difference schemes for the problem of fusing hyperbolic and parabolic equations. Sib. Mat. Zh., 39(4): 854-962. (in Russian); transl. in Sib. Math. J., 39(4): 825-834.
  2. Samarskii, A.A., Korzyuk, V.I., Lemeshevskij, S.V., and Matus, P.P. (1998) Difference schemes for the conjugation problem of a hyperbolic and a parabolic equation on moving grids. Dokl. Ross. Akad. Nauk, 361(3): 321-324. (in Russian); transl. in Dokl. Math., 58(1): 74-77.
  3. Korzyuk, V.I., Lemeshevsky, S.V., and Matus, P.P. (1999) Conjugation problem about jointly separate flow of viscoelastic and viscous fluids in the plane duct. Math. Model. and Analys. (MMA), 4: 114-123.
  4. Samarskii, A.A., Korzyuk, V.I., Lemeshevsky, S.V., and Matus, P.P. (2000) Finite-difference methods for problem of conjugation of hyperbolic and parabolic equations. M3AS: Mathematical Models and Methods in Applied Sciences, 10(3): 361-378.

  1. Matus, P. (2002) Monotone schemes of a higher order of accuracy for differential problems with boundary conditions of the second and third kind. Comp. Meth. Appl. Math, 2(4): 378-391.
  2. Matus, P. and Martsynkevich, G. (2004) Monotone and economical difference schemes on non-uniform grids for multidimensional parabolic equations with boundary conditions of the third kind. Comp. Meth. Appl. Math, 4(3): 350-367.
  3. Matus P. P., Tuyen Vo Thi Kim, Gaspar F. Monotone difference schemes for lin-ear parabolic equations with mixed boundary conditions // Doklady of the Na-tional academy of science of Belarus. – 2014. – V. 58, No. 5, P. 18–22
  4. F.J. Gaspar, F.J. Lisbona, P. Matus, V.T.K. Tuyen Numerical methods for a one-dimensional non-linear Biot’s model // Journal of Computational and Ap-plied Mathematics. –2016. – V. 293, February 2016, P. 62 –72
  5. F.J. Gaspar, F.J. Lisbona, P. Matus, V.T.K. Tuyen Monotone finite difference schemes for quasilinear parabolic problems with mixed boundary conditions // Comp. Meth. Appl. Math. –2016. – Vol. 16. – No. 2. –P. 231-243.

  1. Jovanovich, B., Lemeshevsky, B., and Matus, P. (2002) On the stability of differential-operator equations and operator-difference schemes Comp. Meth. Appl. Math., 2(2): 153-170.
  2. Jovanovich, B.S. and Matus, P.P. (2003) Asymptotic Stability of First- and Second-Order Operator-Differential Equations Differents. Uravneniya, 39(3): 383-392. (in Russian); transl. in Differential Equations, 39(3): 414-425.

  1. Matus P., and Lemeshevsky S.V. (2009) Stability and monotonicity of difference schemes for nonlinear scalar conservation laws and multidimensional quasi-linear parabolic equations Comput. Method Appl. Math. 9(3): 253 - 280.
  2. Matus, P.P. (2010) Stability with respect to the initial data and monotonicity of an implicit difference scheme for a homogeneous porous medium equation with a quadratic nonlinearity Differ. Equ. 46, No. 7, 1019-1029 (in English); translation from Differ. Uravn. 46, No. 7, 1011-1021 (2010).
  3. Matus, P.P. (2010) Well-posedness of difference schemes for semilinear parabolic equations with weak solutions Zh. Vychisl. Mat. Mat. Fiz.50, No. 12, 2155-2175 (in Russian); translation in Comput. Math. Math. Phys. 50, No. 12, 2044-2063 (2010).
  4. Matus, P.P., Lemeshevsky, S., and Kandratsiuk, A. (2010) Well-posedness and blow up for IBVP for semilinear parabolic equations and numerical methods Comput. Meth. Appl. Math. 10(4): 395-420.
  5. Matus, P.P. (2013) On the role of conservation laws in the problem of occurrence of unstable solutions for quasi-linear parabolic equations and their approximations Differ. Equ. 49, No. 7 (in English); translation from Differ. Uravn. 49, No. 7 (2013).
  6. P. P. Matus, N. G. Churbanova, and D. A. Shchadinskii On the Role of Conser-vation Laws and Input Data in the Generation of Peaking Modes in Quasilinear Multidimensional Parabolic Equations with Nonlinear Source and in Their Ap-proximations // Differential Equations. – 2016. – Vol. 52. – No. 7. –P. 942 –950
  7. Matus P.P., Kozera R., Paradzinska A., and Schadinsky D.A. Discrete analogs of the comparison theorem and two-side estimates of solution of parabolic equa-tions // Applied Mathematics & Information Sciences. – 2016. –V. 10, No. 1, P. 83-92.

  1. Matus, P.P. (1990) A class of difference schemes on composite meshes for nonstationary problems of mathematical physics. Differents. Uravneniya, 26(7): 1241-1254. (in Russian); transl. in Differential Equations, 26(7): 911-922.
  2. Matus, P.P. (1991) Construction of difference schemes for multidimensional parabolic equations. Differents. Uravneniya, 27(11): 1961-1971. (in Russian); transl. in Differential Equations, 27(11): 1404-1414.
  3. Matus, P.P. (1993) Conservative finite-difference scheme in subdomains for parabolic and hyperbolic second-order equations. Differents. Uravneniya, 29(4): 700-711. (in Russian); transl. in Differential Equations, 29(4): 595-605.
  4. Matus, P.P. (1993) Conservative difference schemes for quasilinear parabolic equations in subdomains. Differents. Uravneniya, 29(7): 1222-1231. (in Russian); transl. in Differential Equations, 29(7): 1060-1069.
  5. Matus, P.P. and Mikhailuk, I.A. (1993) Difference schemes with variable weights for evolutionary equations of second order. Mathematical Modeling, 5(12): 35-60. (in Russian).
  6. Matus, P.P. (1994) Difference schemes on composite grids for hyperbolic equations. Zh. Vychisl. Mat. Mat. Fiz. 34(6): 870-885; transl. in Comput. Math. Math. Phys., 34(6): 749-761.
  7. Vabishchevich, P.N., Matus, P.P., and Rychagov, V.G. (1995) A class of difference schemes on dynamic locally concentrating grids. Differents. Uravneniya, 31(5): 849-857. (in Russian); transl. in Differential Equations, 31(5): 787-796.
  8. Samarskii, A.A., Vabishchevich, P.N., and Matus, P.P. (1996) Finite-difference approximations of higher accuracy order on nonuniform grids. Differents. Uravneniya, 32(2): 265-274. (in Russian); transl. in Differential Equations, 32(2): 269-281.
  9. Samarskii, A.A., Mazhukin, V.I., Matus, P.P., and Chuiko, M.M. (1996) Invariant finite-difference schemes for equations of mathematical physics in nonstationary coordinate systems. Differents. Uravneniya, 32(12): 1691-1701. (in Russian); transl. in Differential Equations, 32(12): 1685-1695.
  10. Samarskii, A.A., Matus, P.P., and Rychagov, V.G. (1997) Monotone difference schemes of high order on nonuniform grids. Mathematical Modeling, 9(2): 95-96. (in Russian).
  11. Samarskii, A.A., Mazhukin, V.I., and Matus, P.P. (1997) Invariant difference schemes for differential equations with the transformation of independent variables. Dokl. Ross. Akad. Nauk, 352(5): 602-605; transl. in Dokl. Math., 55(1): 140-143.
  12. Samarskii, A.A., Jovanovich, B.S., Matus, P.P., and Shcheglik, V.S. (1997) Finite-difference schemes on adaptive time grids for parabolic equations with generalized solutions. Differents. Uravneniya, 33(7): 975-984. (in Russian); transl. in Differential Equations, 33(7): 981-991.
  13. Samarskii, A.A., Vabishchevich, P.N., and Matus, P.P. (1998) Second-order accurate finite-difference schemes on nonuniform grids. Zh. Vychisl. Mat. Mat. Fiz., 38(3): 413-424. (in Russian); transl. in Comput. Math. Math. Phys., 38(3): 399-410.
  14. Vabishchevich, P.N., Lemeshevskij, S.V., and Matus, P.P. (1998) Difference schemes for the problem of fusing hyperbolic and parabolic equations. Sib. Mat. Zh., 39(4): 854-962. (in Russian); transl. in Sib. Math. J., 39(4): 825-834.
  15. Samarskii, A.A., Mazhukin, V.I., and Matus, P.P. (1998) Finite-difference scheme on nonuniform grids for a two-dimensional parabolic equation. Differents. Uravneniya, 34(7): 980-987. (in Russian); transl. in Differ. Equations, 34(7): 982-990.
  16. Jovanovich, B.S. and Matus, P.P. (1999) Estimation of the convergence rate of difference schemes for elliptic problems. Zh. Vychisl. Mat. Mat. Fiz., 39(1): 61-69. (in Russian); transl. in Comp. Math. Math. Phys., 39(1): 56-64.
  17. Samarskii, A.A., Mazhukin, V.I., Malafei, D.A., and Matus, P.P. (1999) Accuracy enhancement in difference schemes on spatially nonuniform grids. Dokl. Ross. Akad. Nauk, 367(3): 310-313. (in Russian); transl. in Dokl. Math. 60(1): 61-64.
  18. Zyl, A.N. and Matus, P.P. (1999) Efficient high-order accurate finite-difference schemes for multidimensional parabolic equations on nonuniform grids. Zh. Vychisl. Mat. Mat. Fiz., 39(7): 1151-1157. (in Russian); transl. in Comp. Math. Math. Phys., 39(7): 1109-1115.
  19. Samarskii, A.A., Vabishchevich, P.N., Zyl, A.N., and Matus, P.P. (1999) Difference scheme of second order accuracy for Dirichlet problem in a general domain. Math. Modeling, 11(9): 71-82. (in Russian).
  20. Matus, P.P. and Zyl, A.N. (2000) Difference schemes of high order accuracy for mathematical physics problems in arbitrary areas. Mathematical Modeling and Analysis (MMA), 5: 133-142.
  21. Matus, A.P. and Matus, P.P. (2001) The maximum principle and its application for the investigation of stability and convergence of difference schemes. Mathematical Modeling and Analysis (MMA), 6(2): 289-299.
  22. Matus, P.P. and Zjuzina, E.L. (2001) Three-level difference schemes on non-uniform in time grids. Comput. Meth. Appl. Math., 1(3): 265-284.
  23. Samarskii A.A., Matus, P.P., and Vabishchevich, P.N., (2002) Difference schemes with operator factors, Kluwer Academic Publishers, Boston/Dordrecht/London, 384 p.
  24. Matus, P.P. (2002) The maximum principle and some of its applications. Comput. Meth. Appl. Math., 2(1): 50-91.
  25. Matus, P. and Martsynkevich, G. (2004) Monotone and economical difference schemes on non-uniform grids for multidimensional parabolic equations with boundary conditions of the third kind. Comp. Meth. Appl. Math, 4(3): 350-367
  26. P.P. Matus, Le Minh Hieu Difference Schemes on Nonuniform Grids for the Two-Dimensional Convection–Diffusion Equation // Computational Mathemat-ics and Mathematical Physics, 2017, Vol. 57, No. 12, pp. 1994–2004.
  27. П.П. Матус, Л.М. Хиеу Монотонные разностные схемы на неравномер-ных сетках для двумерного квазилинейного уравнения конвекции-диффузии // Доклады НАН Беларуси. – 2017. – Т. 61, № 4. – С. 7–13
  28. Piotr Matus, Le Minh Hieu, Lubin G. Vulkov Analysis of second order differ-ence schemes on non-uniform grids for quasilinear parabolic equations // Jour-nal of Computational and Applied Mathematics. –2017– Vol. 310. – P.186 –199
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