New Difference Schemes for Partial Differential Equations by Allaberen Ashyralyev, Pavel E. Sobolevskii.
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 differenc...
Birkhäuser Basel : Imprint: Birkhäuser,
|Edition:||1st ed. 2004.|
|Series:||Operator Theory: Advances and Applications,
Springer eBook Collection.
|Online Access:||Click to view e-book|
|Holy Cross Note:||Loaded electronically.|
Electronic access restricted to members of the Holy Cross Community.
- 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.