Numerical treatment and analysis of time-fractional evolution equations / Bangti Jin, Zhi Zhou.
Jin, Bangti, author.; Zhou, Zhi, author.
2023
QA377.3
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Title Numerical treatment and analysis of time-fractional evolution equations / Bangti Jin, Zhi Zhou.
Author Jin, Bangti, author.
ISBN 9783031210501 (electronic bk.)
3031210506 (electronic bk.)
3031210492
9783031210495
DOI https://doi.org/10.1007/978-3-031-21050-1
Published Cham, Switzerland : Springer, 2023.
Language English
Description 1 online resource (370 pages) : illustrations (colour).
Item Number 10.1007/978-3-031-21050-1 doi
Call Number QA377.3
Dewey Decimal Classification 515/.353
Summary This book discusses numerical methods for solving time-fractional evolution equations. The approach is based on first discretizing in the spatial variables by the Galerkin finite element method, using piecewise linear trial functions, and then applying suitable time stepping schemes, of the type either convolution quadrature or finite difference. The main concern is on stability and error analysis of approximate solutions, efficient implementation and qualitative properties, under various regularity assumptions on the problem data, using tools from semigroup theory and Laplace transform. The book provides a comprehensive survey on the present ideas and methods of analysis, and it covers most important topics in this active area of research. It is recommended for graduate students and researchers in applied and computational mathematics, particularly numerical analysis.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Added Author Zhou, Zhi, author.
Series Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 214.
Available in Other Form NUMERICAL TREATMENT AND ANALYSIS OF TIME -FRACTIONAL EVOLUTION EQUATIONS.
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Existence, Uniqueness, and Regularity of Solutions
Semidiscrete Discretization
Convolution Quadrature
Finite Difference Methods: Construction and Implementation
Finite Difference Methods on Uniform Meshes
Finite Difference Methods on Graded Meshes
Nonnegativity Preservation
Discrete Fractional Maximal Regularity
Subdiffusion with time-dependent coefficients
Semilinear Subdiffusion Equations
Time-Space Formulation and Finite Element Approximation
A Spectral Petrov-Galerkin Method
Incomplete Iterative Solution at the Time Levels
Optimal Control with Subdiffusion Constraint
Backward Subdiffusion Problems
Appendix: Mathematical Preliminaries.

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