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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.
About the author
Bangti Jin received the B.Eng. degree in polymeric materials and engineering in 2002, the
M.Sc. degree in computational mathematics in 2005, both from Zhejiang University, Hangzhou, China, and the Ph.D. degree in applied mathematics from the Chinese University of Hong Kong, Hong Kong, in 2008. Previously, he was an Assistant Professor of mathematics at the University of California, Riverside (2013-2014), a Visiting Assistant Professor at Texas A&M University (2010-2013), an Alexandre von Humboldt Postdoctoral Researcher at the University of Bremen (2009-2010). He is currently Professor of Inverse Problems at the Department of Computer Science, University College London, London, U.K. His research interests include computational inverse problems and numerical analysis of differential equations.
