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New Difference Schemes for Partial Differential Equations

'Operator Theory: Advances and Applications'. Auflage 2004. Bibliographie. Book.
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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 p… weiterlesen
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Produktdetails

Titel: New Difference Schemes for Partial Differential Equations
Autor/en: Allaberen Ashyralyev, Pavel E. Sobolevskii

ISBN: 3764370548
EAN: 9783764370541
'Operator Theory: Advances and Applications'.
Auflage 2004.
Bibliographie.
Book.
Springer Basel AG

25. Juni 2004 - gebunden - IX

Beschreibung

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.

Inhaltsverzeichnis

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.
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