Numerical Treatment and Analysis of Time-Fractional Evolution Equations

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Numerical Treatment and Analysis of Time-Fractional Evolution Equations is written by Bangti Jin and published by Springer Nature. It's available with International Standard Book Number or ISBN identification 3031210506 (ISBN 10) and 9783031210501 (ISBN 13).

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.