New Difference Schemes for Partial Differential Equations by Allaberen AshyralyevNew Difference Schemes for Partial Differential Equations by Allaberen Ashyralyev

New Difference Schemes for Partial Differential Equations

byAllaberen Ashyralyev, Pavel E. Sobolevskii

Paperback | October 14, 2012

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This book explores new difference schemes for approximating the solutions of regular and singular perturbation boundary-value problems for PDEs. The construction is based on the exact difference scheme and Taylor's decomposition on the two or three points, which permits investigation of differential equations with variable coefficients and regular and singular perturbation boundary value problems.

Title:New Difference Schemes for Partial Differential EquationsFormat:PaperbackDimensions:446 pagesPublished:October 14, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034896220

ISBN - 13:9783034896221

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Table of Contents

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 Taylor'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 Taylor'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 Taylor'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 Taylor'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 Taylor'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.