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Author: Juergen Geiser Publisher: 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
Author: Juergen Geiser Publisher: 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
Author: Helge Holden Publisher: 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.
Author: Pieter Jacobus Houwen Publisher: ISBN: Category : Differential equations Languages : en Pages : 18
Book Description
Abstract: "We consider stiff initial-value problems for second-order differential equations of the special form y"=f(y). Stiff initial-value problem solvers are necessarily implicit, hence, we are faced with the problem of solving systems of implicit relations. This paper focuses on the construction and analysis of iterative solution methods which are effective in cases where the Jacobian of the righthand side of the differential equation can be split into a sum of matrices with a simple structure. These iterative methods consist of the modified Newton method and an iterative linear solver to deal with the linear Newton systems. The linear solver is based on the approximate factorization of the system matrix associated with the linear Newton systems. A number of convergence results are derived for the linear solver in the case where the Jacobian matrix can be split into commuting matrices. Such often [sic] problems arise in the spatial discretization of time-dependent partial differential equations. Furthermore, the stability matrix and the order of accuracy of the integration process are derived in the case of a finite number of iterations."
Author: Juergen Geiser Publisher: 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
Author: Ivan Dimov Publisher: Springer ISBN: 3030115399 Category : Computers Languages : en Pages : 688
Book Description
This book constitutes the refereed conference proceedings of the 7th International Conference on Finite Difference Methods, FDM 2018, held in Lozenetz, Bulgaria, in June 2018.The 69 revised full papers presented together with 11 invited papers were carefully reviewed and selected from 94 submissions. They deal with many modern and new numerical techniques like splitting techniques, Green’s function method, multigrid methods, and immersed interface method.
Author: Juergen Geiser Publisher: Springer ISBN: 3319151177 Category : Technology & Engineering Languages : en Pages : 343
Book Description
This book examines the latest research results from combined multi-component and multi-scale explorations. It provides theory, considers underlying numerical methods and presents brilliant computational experimentation. Engineering computations featured in this monograph further offer particular interest to many researchers, engineers and computational scientists working in frontier modeling and applications of multicomponent and multiscale problems. Professor Geiser gives specific attention to the aspects of decomposing and splitting delicate structures and controlling decomposition and the rationale behind many important applications of multi-component and multi-scale analysis. Multicomponent and Multiscale Systems: Theory, Methods and Applications in Engineering also considers the question of why iterative methods can be powerful and more appropriate for well-balanced multiscale and multicomponent coupled nonlinear problems. The book is ideal for engineers and scientists working in theoretical and applied areas.
Author: Juergen Geiser
Author: Juergen Geiser
Author: Jürgen Geiser
Author: Helge Holden
Author: Jürgen Geiser
Author: Pieter Jacobus Houwen
Author: Juergen Geiser
Author: Yousef Saad
Author: Jürgen Geiser
Author: Ivan Dimov
Author: Juergen Geiser