LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	515
Title	New Difference Schemes for Partial Differential Equations ([EBook] /) / by Allaberen Ashyralyev, Pavel E. Sobolevskii.
Author	Ashyralyev, Allaberen
Added Personal Name	Sobolevskii, Pavel E. author.
Other name(s)	SpringerLink (Online service)
Publication	Basel : : Birkhäuser Basel : : Imprint: Birkhäuser, , 2004.
Physical Details	IX, 446 p. : online resource.
Series	Operator theory : advances and applications ; 148
ISBN	9783034879224
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-7922-4
Links to Related Works	Subject References: Algebra . Analysis . Analysis (Mathematics) . Functional Analysis . Mathematical analysis . Mathematics . Numerical Analysis . Operator Theory . Partial differential equations . Authors: Ashyralyev, Allaberen . Sobolevskii, Pavel E. . Corporate Authors: SpringerLink (Online service) . Series: Operator theory : advances and applications . Classification: 515 .

Catalogue Display

New Difference Schemes for Partial Differential Equations

Reviews