Numerical Treatment and Analysis of Time-Fractional Evolution Equations

Numerical Treatment and Analysis of Time-Fractional Evolution Equations

Author
Bangti Jin, Zhi Zhou
Publisher
Springer
Language
English
Year
2023
Page
427
ISBN
3031210492,9783031210495
File Type
pdf
File Size
3.8 MiB

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.

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