Well-Posedness of Parabolic Difference Equations (Operator Theory Advances & Applications) - Hardcover

Allaberen Ashyralyev; Pavel E. Sobolevskii

Hardcover

ISBN 10: 0817650245 ISBN 13: 9780817650247

Publisher: Birkhauser, 1994

Synopsis

A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Modern computers allow the implementation of highly accurate ones; hence, their construction and investigation for various boundary value problems in mathematical physics is generating much current interest. The present monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on Padé approximations. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Establishing coercivity inequalities allows one to obtain sharp, that is, two-sided estimates of convergence rates. The proofs are based on results in interpolation theory of linear operators. This monograph will be of value to professional mathematicians as well as advanced students interested in the fields of functional analysis and partial differential equations.

About this title

Language Notes

Text: English (translation)
Original Language: Russian

Edition details

• Publisher: Birkhauser
• Publication date: 1994
• ISBN 10: 0817650245
• ISBN 13: 9780817650247
• Binding: Hardcover
• Language: English
• Number of pages: 368