---

＜電子ブック＞
New Difference Schemes for Partial Differential Equations / by Allaberen Ashyralyev, Pavel E. Sobolevskii
(Operator Theory: Advances and Applications. ISSN:22964878 ; 148)

版	1st ed. 2004.
出版者	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
出版年	2004
本文言語	英語
大きさ	IX, 446 p : online resource
著者標目	*Ashyralyev, Allaberen author Sobolevskii, Pavel E author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Operator theory LCSH:Algebra LCSH:Functional analysis LCSH:Differential equations LCSH:Numerical analysis FREE:Analysis FREE:Operator Theory FREE:Algebra FREE:Functional Analysis FREE:Differential Equations FREE:Numerical Analysis
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-0348-7922-4

 類似資料