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AuthorAshyralyev, Allaberen. author
TitleNew Difference Schemes for Partial Differential Equations [electronic resource] / by Allaberen Ashyralyev, Pavel E. Sobolevskii
ImprintBasel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2004
Connect tohttp://dx.doi.org/10.1007/978-3-0348-7922-4
Descript IX, 446 p. online resource

SUMMARY

The present monograph is devoted to the construction and investigation of the new high order of accuracy difference schemes of approximating the solutions of regular and singular perturbation boundary value problems for partial differential equations. The construction is based on the exact difference scheme and Taylor's decomposition on the two or three points. This approach permitted essentially to extend to a class of problems where the theory of difference methods is applicable. Namely, now it is possible to investigate the differential equations with variable coefficients and regular and singular perturbation boundary value problems. The investigation is based on new coercivity inequalities. The book will be of value to professional mathematicians, as well as advanced students in the fields of numerical analysis, functional analysis, and ordinary and partial differential equations


CONTENT

1 Linear Difference Equations -- 1.1 Difference Equations of the First Order -- 1.2 Difference Equations of the Second Order -- 1.3 Difference Equations with Constant Coefficients -- 2 Difference Schemes for First-Order Differential Equations -- 2.1 Single-Step Exact Difference Scheme and Its Applications -- 2.2 Taylorโ{128}{153}s Decomposition on Two Points and Its Applications -- 3 Difference Schemes for Second-Order Differential Equations -- 3.1 Two-Step Exact Difference Scheme and Its Applications -- 3.2 Taylorโ{128}{153}s Decomposition on Three Points and Its Applications -- 4 Partial Differential Equations of Parabolic Type -- 4.1 A Cauchy Problem. Well-posedness -- 4.2 Difference Schemes Generated by an Exact Difference Scheme -- 4.3 Single-Step Difference Schemes Generated by Taylorโ{128}{153}s Decomposition -- 5 Partial Differential Equations of Elliptic Type -- 5.1 A Boundary-Value Problem. Well-posedness -- 5.2 Difference Schemes Generated by an Exact Difference Scheme -- 5.3 Two-Step Difference Schemes Generated by Taylorโ{128}{153}s Decomposition -- 6 Partial Differential Equations of Hyperbolic Type -- 6.1 A Cauchy Problem -- 6.2 Difference Schemes Generated by an Exact Difference Scheme -- 6.3 Two-Step Difference Schemes Generated by Taylorโ{128}{153}s Decomposition -- 7 Uniform Difference Schemes for Perturbation Problems -- 7.1 A Cauchy Problem for Parabolic Equations -- 7.2 A Boundary-Value Problem for Elliptic Equations -- 7.3 A Cauchy Problem for Hyperbolic Equations -- 8 Appendix: Delay Parabolic Differential Equations -- 8.1 The Initial-Value Differential Problem -- 8.2 The Difference Schemes -- Comments on the Literature


Mathematics Algebra Mathematical analysis Analysis (Mathematics) Functional analysis Operator theory Partial differential equations Numerical analysis Mathematics Analysis Operator Theory Algebra Functional Analysis Partial Differential Equations Numerical Analysis



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