Details

Subject(s)

• Evolution equations [Browse]
• Fractional differential equations [Browse]

Author

• Zhou, Zhi [Browse]

Series

• Applied mathematical sciences (Springer-Verlag New York Inc.) ; 214. [More in this series]
• Applied mathematical sciences ; 214

Summary note

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.

Bibliographic references

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

Rights and reproductions note

Current copyright fee: GBP19.00 42\0.

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.

Show 15 more Contents items

ISBN

• 3031210492 ((hbk.))
• 9783031210495 ((hbk.))

OCLC

1347260792

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