New Difference Schemes for Partial Differential Equations
By: by Allaberen Ashyralyev, Pavel E. Sobolevskii
Contributors: Sobolevskii, Pavel E.
Series: Operator Theory: Advances and Applications -- 148; Operator theory, advances and applications -- 148.
Publisher: Birkhäuser Basel; Imprint; Birkhäuser
Published: 2004
Place of publication: Basel
Language: eng
Format: [electronic resource] /
Number of pages: 443
ISBN-13: 9783034879224
Subjects: Numerical analysis; Algebra; Functional analysis; Mathematics; Operator theory; Differential equations, partial
Description: 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.