Bangti Jin's Books

Fractional Differential Equations

An Approach via Fractional Derivatives

By: Bangti Jin

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Fractional Differential Equations

An Approach via Fractional Derivatives

By: Bangti Jin

This graduate textbook provides a self-contained introduction to modern mathematical theory on fractional differential equations. It addresses both ordinary and partial differential equations with a focus on detailed solution theory, especially regularity theory under realistic assumptions on the problem data. The text includes an extensive bibliography, application-driven modeling, extensive exercises, and graphic illustrations throughout to complement its comprehensive presentation of the field. It is recommended for graduate students and researchers in applied and computational mathematics, particularly applied analysis, numerical analysis and inverse problems.

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Page Count

377

Publisher

Springer Nature

Published Date

ISBN 10

303076043X

ISBN 13

9783030760434

Inverse Problems: Tikhonov Theory And Algorithms

By: Kazufumi Ito,Bangti Jin

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Inverse Problems: Tikhonov Theory And Algorithms

By: Kazufumi Ito,Bangti Jin

Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. The mathematical theory focuses on nonsmooth Tikhonov regularization for linear and nonlinear inverse problems. The computational methods include nonsmooth optimization algorithms, direct inversion methods and uncertainty quantification via Bayesian inference.The book offers a comprehensive treatment of modern techniques, and seamlessly blends regularization theory with computational methods, which is essential for developing accurate and efficient inversion algorithms for many practical inverse problems.It demonstrates many current developments in the field of computational inversion, such as value function calculus, augmented Tikhonov regularization, multi-parameter Tikhonov regularization, semismooth Newton method, direct sampling method, uncertainty quantification and approximate Bayesian inference. It is written for graduate students and researchers in mathematics, natural science and engineering.

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Page Count

330

Publisher

World Scientific

Published Date

ISBN 10

9814596213

ISBN 13

9789814596213

Numerical Treatment and Analysis of Time-Fractional Evolution Equations

By: Bangti Jin,Zhi Zhou

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Numerical Treatment and Analysis of Time-Fractional Evolution Equations

By: Bangti Jin,Zhi Zhou

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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Page Count

428

Publisher

Springer Nature

Published Date

ISBN 10

3031210506

ISBN 13

9783031210501

Book's by Bangti Jin

Fractional Differential Equations

Fractional Differential Equations

Inverse Problems: Tikhonov Theory And Algorithms

Inverse Problems: Tikhonov Theory And Algorithms

Numerical Treatment and Analysis of Time-Fractional Evolution Equations

Numerical Treatment and Analysis of Time-Fractional Evolution Equations

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