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New Difference Schemes for Partial Differential Equations

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...

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Bibliographic Details
Main Authors: Ashyralyev, Allaberen, Sobolevskii, Pavel E. (Author)
Format: eBook
Language:English
Published: Basel Birkhäuser 2004, 2004
Edition:1st ed. 2004
Series:Operator Theory: Advances and Applications
Subjects:
Functional Analysis
Numerical Analysis
Mathematical Analysis
Analysis
Algebra
Operator Theory
Differential Equations
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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

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