Numerical Treatment and Analysis of Time-Fractional Evolution Equations
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Beschreibung
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.
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.
Provides insight in the mathematics of numerical methods for solving time-fractional evolution equations Presents ideas and methods of analysis, and covers most important topics in this active area of research For graduate students and researchers in applied and computational mathematics, numerical analysis.
Autor*in
Bangti Jin
Themen in »Numerical Treatment and Analysis of Time-Fractional Evolution Equations«
time-fractional diffusion equation Galerkin method differential equation finite element method convolution quadrature maximal regularity Laplace transform error analysis nonsmooth solution