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Numerical treatment and analysis of ...

Jin, Bangti.

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Numerical treatment and analysis of time-fractional evolution equations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Numerical treatment and analysis of time-fractional evolution equations/ by Bangti Jin, Zhi Zhou.
作者:	Jin, Bangti.
其他作者:	Zhou, Zhi.
出版者:	Cham :Springer International Publishing : : 2023.,
面頁冊數:	xiii, 427 p. :ill., digital ;24 cm.
內容註:	Existence, Uniqueness, and Regularity of Solutions -- Semidiscrete Discretization -- Convolution Quadrature -- Finite Difference Methods: Construction and Implementation -- Finite Difference Methods on Uniform Meshes -- Finite Difference Methods on Graded Meshes -- Nonnegativity Preservation -- Discrete Fractional Maximal Regularity -- Subdiffusion with time-dependent coefficients -- Semilinear Subdiffusion Equations -- Time-Space Formulation and Finite Element Approximation -- A Spectral Petrov-Galerkin Method -- Incomplete Iterative Solution at the Time Levels -- Optimal Control with Subdiffusion Constraint -- Backward Subdiffusion Problems -- Appendix: Mathematical Preliminaries.
Contained By:	Springer Nature eBook
標題:	Evolution equations. -
電子資源:	https://doi.org/10.1007/978-3-031-21050-1
ISBN:	9783031210501

Numerical treatment and analysis of time-fractional evolution equations
Jin, Bangti.

Numerical treatment and analysis of time-fractional evolution equations[electronic resource] /by Bangti Jin, Zhi Zhou. - Cham :Springer International Publishing :2023. - xiii, 427 p. :ill., digital ;24 cm. - Applied mathematical sciences,v. 2142196-968X ;. - Applied mathematical sciences ;v. 214..

Existence, Uniqueness, and Regularity of Solutions -- Semidiscrete Discretization -- Convolution Quadrature -- Finite Difference Methods: Construction and Implementation -- Finite Difference Methods on Uniform Meshes -- Finite Difference Methods on Graded Meshes -- Nonnegativity Preservation -- Discrete Fractional Maximal Regularity -- Subdiffusion with time-dependent coefficients -- Semilinear Subdiffusion Equations -- Time-Space Formulation and Finite Element Approximation -- A Spectral Petrov-Galerkin Method -- Incomplete Iterative Solution at the Time Levels -- Optimal Control with Subdiffusion Constraint -- Backward Subdiffusion Problems -- Appendix: Mathematical Preliminaries.

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.

ISBN: 9783031210501

Standard No.: 10.1007/978-3-031-21050-1doiSubjects--Topical Terms:

663081
Evolution equations.

LC Class. No.: QA1

Dewey Class. No.: 515.353

Numerical treatment and analysis of time-fractional evolution equations
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505 0 $a Existence, Uniqueness, and Regularity of Solutions -- Semidiscrete Discretization -- Convolution Quadrature -- Finite Difference Methods: Construction and Implementation -- Finite Difference Methods on Uniform Meshes -- Finite Difference Methods on Graded Meshes -- Nonnegativity Preservation -- Discrete Fractional Maximal Regularity -- Subdiffusion with time-dependent coefficients -- Semilinear Subdiffusion Equations -- Time-Space Formulation and Finite Element Approximation -- A Spectral Petrov-Galerkin Method -- Incomplete Iterative Solution at the Time Levels -- Optimal Control with Subdiffusion Constraint -- Backward Subdiffusion Problems -- Appendix: Mathematical Preliminaries.
520 $a 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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