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A new class of difference schemes with operator factors that includes the schemes with variable weighting factors is picked out in the monograph. The theory of stability is developed for such two- and three-level difference schemes with non-selfadjoint operators. On the basis of general results obtained, the stability and convergence investigation of various initial boundary-value problems for equations with partial derivatives was realized. Adaptive difference schemes with time and spatial thickening are constructed. A theoretical analysis of domain-additive difference schemes (domain decomposition schemes) that are oriented on the construction of effective computational algorithms for parallel computer systems is realized. The book is intended for specialists in numerical methods of solution of mathematical physics problems; the exposition is easily understood by senior students of universities. |
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View the Contents, Introduction&References, and Index. |