Numerical Solution of Partial Differential Equations

An Introduction

K. W. Morton, D. F. Mayers

• Publisher: Cambridge University Press
• Year: 2005
• Print ISBN: 9780521607933
• eBook ISBN: 9780511110306
• Edition: 2
• Topic: Mathematics
• Subtopic: Mathematical Analysis
• Index: Mathematics

This is the 2005 second edition of a highly successful and well-respected textbook on the numerical techniques used to solve partial differential equations arising from mathematical models in science, engineering and other fields. The authors maintain an emphasis on finite difference methods for simple but representative examples of parabolic, hyperbolic and elliptic equations from the first edition. However this is augmented by new sections on finite volume methods, modified equation analysis, symplectic integration schemes, convection-diffusion problems, multigrid, and conjugate gradient methods; and several sections, including that on the energy method of analysis, have been extensively rewritten to reflect modern developments. Already an excellent choice for students and teachers in mathematics, engineering and computer science departments, the revised text includes more latest theoretical and industrial developments.

Table of contents

• Cover
• Half-title
• Title
• Copyright
• Contents
• Preface to the first edition
• Preface to the second edition
• 1 Introduction
• 2 Parabolic equations in one space variable
• 3 Parabolic equations in two and three dimensions
• 4 Hyperbolic equations in one space dimension
• 5 Consistency, convergence and stability
• 6 Linear second order elliptic equations in two dimensions
• 7 Iterative solution of linear algebraic equations
• References
• Index