Numerical treatment and analysis of time-fractional evolution equations / Bangti Jin, Zhi Zhou

Format:

Book

Author/Creator:

Jin, Bangti, author.

Zhou, Zhi (Researcher in numerical analysis), author.

Series:

Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 214.

Applied mathematical sciences, 0066-5452 ; 214

Language:

English

Subjects (All):

Evolution equations.

Fractional differential equations.

Physical Description:

xiii, 427 pages ; 25 cm

Place of Publication:

Cham, Switzerland : Springer, [2023]

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--back cover.

Contents:

1. Existence, Uniqueness, and Regularity of Solutions

2. Spatially Semidiscrete Discretization

3. Convolution Quadrature

4. Finite Difference Methods: Construction and Implementation

5. Finite Difference Methods on Uniform Meshes

6. Finite Difference Methods on Graded Meshes

7. Nonnegativity Preservation

8. Discrete Maximal Regularity

9. Subdiffusion with Time-Dependent Coefficients

10. Semilinear Subdiffusion

11. Time-Space Finite Element Approximation

12. Spectral Galerkin Approximation

13. Incomplete Iterative Solution at Time Levels

14. Optimal Control with Subdiffusion Constraint

15. Backward Subdiffusion

Appendix A: Mathematical Preliminaries

References

Index.

Notes:

Current copyright fee: GBP19.00 42\0.

Includes bibliographical references (pages 411-423) and index.

ISBN:

3031210492

9783031210495

OCLC:

1347260792