New Difference Schemes for Partial Differential Equations

✍ Scribed by Allaberen Ashyralyev, Pavel E. Sobolevskii (auth.)

• Publisher: Birkhäuser Basel
• Year: 2004
• Tongue: English
• Leaves: 452
• Series: Operator Theory: Advances and Applications 148
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-ix
Linear Difference Equations....Pages 1-10
Difference Schemes for First-Order Differential Equations....Pages 11-35
Difference Schemes for Second-Order Differential Equations....Pages 37-98
Partial Differential Equations of Parabolic Type....Pages 99-196
Partial Differential Equations of Elliptic Type....Pages 197-311
Partial Differential Equations of Hyperbolic Type....Pages 313-342
Uniform Difference Schemes for Perturbation Problems....Pages 343-392
Appendix: Delay Parabolic Differential Equations....Pages 393-410
Back Matter....Pages 411-446

✦ Subjects

Operator Theory; Algebra; Functional Analysis; Partial Differential Equations; Numerical Analysis