Author: Jürgen GeiserPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Iterative Operator Splitting Methods for Differential Equations
Iterative Operator-splitting Methods for Nonlinear Differential Equations and Applications of Deposition Processes
Author: Jürgen GeiserIterative Splitting Methods for Differential Equations
Author: Juergen GeiserPublisher: Chapman and Hall/CRC
ISBN: 9781439869826
Category : Mathematics
Languages : en
Pages : 0
Book Description
Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential equations and spatial- and time-dependent differential equations. The practical part of the text applies the methods to benchmark and real-life problems, such as waste disposal, elastics wave propagation, and complex flow phenomena. The book also examines the benefits of equation decomposition. It concludes with a discussion on several useful software packages, including r3t and FIDOS. Covering a wide range of theoretical and practical issues in multiphysics and multiscale problems, this book explores the benefits of using iterative splitting schemes to solve physical problems. It illustrates how iterative operator splitting methods are excellent decomposition methods for obtaining higher-order accuracy.
Iterative Splitting Methods for Differential Equations
Author: Juergen GeiserPublisher: CRC Press
ISBN: 1439869839
Category : Mathematics
Languages : en
Pages : 325
Book Description
Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations.In th
Nonlinear Iterative Operator-Splitting Methods and Applications for Nonlinear Parabolic Partial Differential Equations
Author: Jürgen GeiserSplitting Methods for Partial Differential Equations with Rough Solutions
Author: Helge HoldenPublisher: European Mathematical Society
ISBN: 9783037190784
Category : Mathematics
Languages : en
Pages : 238
Book Description
Operator splitting (or the fractional steps method) is a very common tool to analyze nonlinear partial differential equations both numerically and analytically. By applying operator splitting to a complicated model one can often split it into simpler problems that can be analyzed separately. In this book one studies operator splitting for a family of nonlinear evolution equations, including hyperbolic conservation laws and degenerate convection-diffusion equations. Common for these equations is the prevalence of rough, or non-smooth, solutions, e.g., shocks. Rigorous analysis is presented, showing that both semi-discrete and fully discrete splitting methods converge. For conservation laws, sharp error estimates are provided and for convection-diffusion equations one discusses a priori and a posteriori correction of entropy errors introduced by the splitting. Numerical methods include finite difference and finite volume methods as well as front tracking. The theory is illustrated by numerous examples. There is a dedicated Web page that provides MATLABR codes for many of the examples. The book is suitable for graduate students and researchers in pure and applied mathematics, physics, and engineering.
Iterative Operator Splitting Methods with Higher Order Time Integration Methods and Applications for Parabolic Partial Differential Equations
Author: Jürgen GeiserSplitting Methods in Communication, Imaging, Science, and Engineering
Author: Roland GlowinskiPublisher: Springer
ISBN: 3319415891
Category : Mathematics
Languages : en
Pages : 822
Book Description
This book is about computational methods based on operator splitting. It consists of twenty-three chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the cross-fertilization of ideas.
Decomposition Methods for Differential Equations
Author: Juergen GeiserPublisher: CRC Press
ISBN: 1439810974
Category : Mathematics
Languages : en
Pages : 320
Book Description
Decomposition Methods for Differential Equations: Theory and Applications describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It covers real-life problems, the underlying decomposition and discretization, the stability and consistency analysis of the decomposition methods, and num
Decomposition Methods for Differential Equations
Author: Juergen GeiserPublisher:
ISBN: 9781138114142
Category :
Languages : en
Pages : 0
Book Description
Exploring iterative operator-splitting methods, this work describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It generalizes the numerical analysis with respect to the consistency and stability to nonlinear, stiff, and spatial decomposed splitting problems. The book focuses on parabolic and hyperbolic equations, including convection-diffusion-reaction, heat, and wave equations, and applies the results to computational science issues, such as flow problems, elastic-wave propagation, heat transfer, and micromagnetic problems. Software tools are listed in an appendix.