Numerical Treatment and Analysis of Time-F...

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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.

Zusammenfassung

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.

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2023
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Applied Mathematical Sciences
Inhalt:	xiii 427 S. 1 s/w Illustr. 2 farbige Illustr. 427 p. 3 illus. 2 illus. in color.
ISBN-13:	9783031210495
ISBN-10:	3031210492
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Zhou, Zhi Jin, Bangti
Hersteller:	Springer International Publishing Springer International Publishing AG Applied Mathematical Sciences
Maße:	241 x 160 x 30 mm
Von/Mit:	Zhi Zhou (u. a.)
Erscheinungsdatum:	28.02.2023
Gewicht:	0,828 kg