Numerical Methods for Partial Differential Equations - 1st Edition - ISBN: 9780125460507, 9781483262550

Numerical Methods for Partial Differential Equations

1st Edition

Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin-Madison, October 23-25, 1978

Editors: Seymour V. Parter
eBook ISBN: 9781483262550
Imprint: Academic Press
Published Date: 28th January 1979
Page Count: 342
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Description

Numerical Methods for Partial Differential Equations is a collection of papers dealing with techniques and practical solutions to problems concerning continuum mechanics, fluid dynamics, and plasma physics. One paper discusses the important considerations that lead to an efficient nonlinear dynamic finite element analysis using improved analysis techniques. Another paper describes the results obtained from fully discrete methods of higher order in time (order 3 and 4) for second order parabolic initial boundary value problems in which the equations have time dependent (or nonlinear) coefficients. Another paper reviews concepts of ellipticity of finite-difference approximations to general elliptic partial differential systems, with examples utilizing Cauchy-Riemann equations or Navier-Stokes equations. One paper describes fluid-dynamic computing using basic equations, boundary conditions, time dependent gas dynamics, shock waves, stream-function-vorticity methods, and an example on the formation of a spherical vortex. Another paper evaluates a specific problem arising in the study of the equilibrium of plasma confined in a machine of the Tokomak type. The collection is suitable for mathematicians, physicists, and investigators in the field of continuum mechanics, fluid dynamics, plasma physics.

Table of Contents


Contributors

Preface

Finite Element Formulation, Modeling, and Solution of Nonlinear Dynamic Problems

Discrete Methods for Parabolic Equations with Time-Dependent Coefficients

Multigrid Solutions to Elliptic Flow Problems

Computational Fluid Dynamics

The Numerical Solution of a Degenerate Variational Inequality

Simplified Solution Algorithms for Fluid Flow Problems

Numerical Methods for Hyperbolic Partial Differential Equations

Constructing Stable Difference Methods for Hyperbolic Equations

Spectral Methods for Problems in Complex Geometries

Numerical Problems in Plasma Physics

Index

Details

No. of pages:
342
Language:
English
Copyright:
© Academic Press 1979
Published:
Imprint:
Academic Press
eBook ISBN:
9781483262550

About the Editor

Seymour V. Parter