Well-Posedness of Parabolic Difference Equations
By: by A. Ashyralyev, P. E. Sobolevskii
Contributors: Sobolevskiĭ, P. I. (Pavel Iosifovich)
Series: Operator Theory Advances and Applications -- 69; Operator theory, advances and applications -- 69.
Publisher: Birkhäuser Basel; Imprint: Birkhäuser
Published: 1994
Place of publication: Basel
Language: eng
Format: [electronic resource] /
Number of pages: 353
ISBN-13: 9783034896610; 9783034885188
Subjects: Mathematics; Numerical analysis; Global analysis (Mathematics)
Description: 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.
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