Author: E. Jan W. ter MatenPublisher:
ISBN:
Category :
Languages : en
Pages : 24
Book Description
Splitting Methods for Fourth Order Parabolic Partial Differential Equations
Author: E. Jan W. ter MatenSplitting 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 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
Higher Order Parallel Splitting Methods for Parabolic Partial Differential Equations
Author: Malik Shahadat Ali TajNumerical Partial Differential Equations: Finite Difference Methods
Author: J.W. ThomasPublisher: Springer Science & Business Media
ISBN: 0387979999
Category : Mathematics
Languages : en
Pages : 460
Book Description
What makes this book stand out from the competition is that it is more computational. Once done with both volumes, readers will have the tools to attack a wider variety of problems than those worked out in the competitors' books. The author stresses the use of technology throughout the text, allowing students to utilize it as much as possible.
Nonlinear Iterative Operator-Splitting Methods and Applications for Nonlinear Parabolic Partial Differential Equations
Author: Jürgen GeiserNumerical Methods for Partial Differential Equations
Author: William F. AmesPublisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 316
Book Description
Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations
Author: Victor A. GalaktionovPublisher: CRC Press
ISBN: 1482251736
Category : Mathematics
Languages : en
Pages : 565
Book Description
Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.The book
The Finite Difference Method in Partial Differential Equations
Author: A. R. MitchellPublisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 294
Book Description
Extensively revised edition of Computational Methods in Partial Differential Equations. A more general approach has been adopted for the splitting of operators for parabolic and hyperbolic equations to include Richtmyer and Strang type splittings in addition to alternating direction implicit and locally one dimensional methods. A description of the now standard factorization and SOR/ADI iterative techniques for solving elliptic difference equations has been supplemented with an account or preconditioned conjugate gradient methods which are currently gaining in popularity. Prominence is also given to the Galerkin method using different test and trial functions as a means of constructing difference approximations to both elliptic and time dependent problems. The applications of finite difference methods have been revised and contain examples involving the treatment of singularities in elliptic equations, free and moving boundary problems, as well as modern developments in computational fluid dynamics. Emphasis throughout is on clear exposition of the construction and solution of difference equations. Material is reinforced with theoretical results when appropriate.
Partial Differential Equations
Author: Walter A. StraussPublisher: John Wiley & Sons
ISBN: 0470054565
Category : Mathematics
Languages : en
Pages : 467
Book Description
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.