Numerical Methods for Evolutionary Differential Equations / Uri M. Ascher ; Society for Industrial and Applied Mathematics, contributor.

Format:

Book

Author/Creator:

Ascher, U. M. (Uri M.), 1946- author.

Contributor:

Society for Industrial and Applied Mathematics, contributor.

Series:

Computational science and engineering ; 5.

Computational science and engineering ; 5

Language:

English

Subjects (All):

Evolution equations--Numerical solutions.

Physical Description:

1 online resource (xiii, 395 pages) : illustrations (some color).

Place of Publication:

Philadelphia : Society for Industrial and Applied Mathematics, 2008.

Summary:

Methods for the numerical simulation of dynamic mathematical models have been the focus of intensive research for well over 60 years, and the demand for better and more efficient methods has grown as the range of applications has increased. Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary differential equations (ODEs) arise in diverse applications such as fluid flow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical finance. This textbook develops, analyzes, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified viewpoint. The author emphasizes finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and nonsmooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is included as well. Audience: suitable for researchers and graduate students from a variety of fields including computer science, applied mathematics, physics, earth and ocean sciences, and various engineering disciplines. Researchers who simulate processes that are modeled by evolutionary differential equations will find material on the principles underlying the appropriate method to use and the pitfalls that accompany each method.

Contents:

Introduction

Methods and concepts for ODEs

Finite difference and finite volume methods

Stability for constant coefficient problems

Variable coefficient and nonlinear problems

Hamiltonian systems and long time integration

Dispersion and dissipation

More on handling boundary conditions

Several space variables and splitting methods

Discontinuities and almost discontinuities

Additional topics.

Notes:

Description based on print version record.

Includes bibliographical references and index.

ISBN:

0-89871-891-0