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Splitting Methods for Partial Differential Equations with Rough Solutions

2010 Mathematics
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Release : 2010
Genre : Mathematics
Kind : eBook
Book Rating : 784/5 ( reviews)

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Book Synopsis Splitting Methods for Partial Differential Equations with Rough Solutions by : Helge Holden

Download or read book Splitting Methods for Partial Differential Equations with Rough Solutions written by Helge Holden. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: 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 Splitting Methods for Differential Equations

2011-06-01 Mathematics
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Release : 2011-06-01
Genre : Mathematics
Kind : eBook
Book Rating : 839/5 ( reviews)

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Book Synopsis Iterative Splitting Methods for Differential Equations by : Juergen Geiser

Download or read book Iterative Splitting Methods for Differential Equations written by Juergen Geiser. This book was released on 2011-06-01. Available in PDF, EPUB and Kindle. Book excerpt: 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

Time-split Methods for Partial Differential Equations

1982 Differential equations, Hyperbolic
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Release : 1982
Genre : Differential equations, Hyperbolic
Kind : eBook
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Book Synopsis Time-split Methods for Partial Differential Equations by : Randall J. LeVeque

Download or read book Time-split Methods for Partial Differential Equations written by Randall J. LeVeque. This book was released on 1982. Available in PDF, EPUB and Kindle. Book excerpt: This thesis concerns the use of time-split methods for the numerical solution of time-dependent partial differential equations. Frequently the differential operator splits additively into two or more pieces such that the corresponding subproblems are each easier to solve than the original equation, or are best handled by different techniques. In the time-split method the solution to the original equation is advanced by alternately solving the subproblems. In this thesis a unified approach to splitting methods is developed which simplifies their analysis. Particular emphasis is given to splittings of hyperbolic problems into subproblems with disparate wave speeds. Three main aspects of the method are considered. The first is the accuracy and efficiency of the time-split method relative to unsplit methods. The second topic is stability for split methods. The final topic is the proper specification of boundary data for the intermediate solutions, e.g., the solution obtained after solving only one of the subproblems. The main emphasis is on hyperbolic problems, and the one-dimensional shallow water equations are used as a specific example throughout. The final chapter is devoted to some other applications or the theory. Two-dimensional hyperbolic problems, convection-diffusion equations, and the Peaceman-Rachford ADI method for the heat equation are considered.

Splitting Methods for the Numerical Solution of the Incompressible Navier-Stokes Equations

1984
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Release : 1984
Genre :
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Book Synopsis Splitting Methods for the Numerical Solution of the Incompressible Navier-Stokes Equations by : R. Glowinski

Download or read book Splitting Methods for the Numerical Solution of the Incompressible Navier-Stokes Equations written by R. Glowinski. This book was released on 1984. Available in PDF, EPUB and Kindle. Book excerpt: Splitting methods provide efficient tools for solving linear and nonlinear time dependent problems modelled by partial differential equations. In this report we discuss the numerical solution of the Navier-Stokes equations for incompressible viscous fluids by such methods. The splitting permits decoupling the two main difficulties in the problem, namely the nonlinearity and the incompressibility. Actually these splitting methods have a broad range of applicability and can be applied for example, to the solution of eigenvalue problems. Originator supplied keywords include: operator splitting methods, nonlinear least squares, preconditioned conjugate gradient algorithms, finite element approximations, eigenvalue calculation, and variational methods.

Splitting Methods for Fourth Order Parabolic Partial Differential Equations

1982
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Release : 1982
Genre :
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Book Synopsis Splitting Methods for Fourth Order Parabolic Partial Differential Equations by : E. Jan W. ter Maten

Download or read book Splitting Methods for Fourth Order Parabolic Partial Differential Equations written by E. Jan W. ter Maten. This book was released on 1982. Available in PDF, EPUB and Kindle. Book excerpt:

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