Adaptive Method of Lines: 1st Edition (Hardback) book cover

Adaptive Method of Lines

1st Edition

Edited by A, Vande Wouwer, Ph. Saucez, W.E. Schiesser

Chapman and Hall/CRC

432 pages | 50 B/W Illus.

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Hardback: 9781584882312
pub: 2001-04-18
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Description

The general Method of Lines (MOL) procedure provides a flexible format for the solution of all the major classes of partial differential equations (PDEs) and is particularly well suited to evolutionary, nonlinear wave PDEs. Despite its utility, however, there are relatively few texts that explore it at a more advanced level and reflect the method's current state of development.

Written by distinguished researchers in the field, Adaptive Method of Lines reflects the diversity of techniques and applications related to the MOL. Most of its chapters focus on a particular application but also provide a discussion of underlying philosophy and technique. Particular attention is paid to the concept of both temporal and spatial adaptivity in solving time-dependent PDEs. Many important ideas and methods are introduced, including moving grids and grid refinement, static and dynamic gridding, the equidistribution principle and the concept of a monitor function, the minimization of a functional, and the moving finite element method. Applications addressed include shallow water flow, combustion and flame propagation, transport in porous media, gas dynamics, chemical engineering processes, solitary waves, and magnetohydrodynamics.

As the first advanced text to represent the modern era of the method of lines, this monograph offers an outstanding opportunity to discover new concepts, learn new techniques, and explore a wide range of applications.

Table of Contents

Introduction

Application of the Adaptive Method of Lines to Nonlinear Wave Propagation Problems

Adaptive MOL for Magneto-Hydrodynamic PDE Models

Development of a 1-D Error-Minimizing Moving Adaptive Grid Method

An Adaptive Method of Lines Approach for Modelling Flow and Transport in Rivers

An Adaptive Mesh Algorithm for Free Surface Flows in General Geometries, M. Sussman

The Solution of Steady PDEs on Adjustable Meshes in Multidimensions Using Local Descent Methods

Adaptive Linearly Implicit Methods for Heat and Mass Transfer Problems

Linearly Implicit Adaptive Schemes for Singular Reaction-Diffusion Equations

Unstructured Mesh MOL Solvers for Reacting Flow Problems

Two-Dimensional Model of a Reaction Bonded Aluminum Oxide Cylinder

Method of Lines within the Simulation Environment DIVA for Chemical Processes.

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations