Numerical Methods for Partial Differential Equations

William F. Ames, Werner Rheinboldt, Alan Jeffrey

• Publisher: Academic Press
• Year: 2014
• ISBN:
  9781483262420
• Edition: 2
• Topic: Mathematics
• Subtopic: Mathematical Analysis
• Index: Mathematics

Numerical Methods for Partial Differential Equations, Second Edition deals with the use of numerical methods to solve partial differential equations. In addition to numerical fluid mechanics, hopscotch and other explicit-implicit methods are also considered, along with Monte Carlo techniques, lines, fast Fourier transform, and fractional steps methods. Comprised of six chapters, this volume begins with an introduction to numerical calculation, paying particular attention to the classification of equations and physical problems, asymptotics, discrete methods, and dimensionless forms. Subsequent chapters focus on parabolic and hyperbolic equations, elliptic equations, and special topics ranging from singularities and shocks to Navier-Stokes equations and Monte Carlo methods. The final chapter discuss the general concepts of weighted residuals, with emphasis on orthogonal collocation and the Bubnov-Galerkin method. The latter procedure is used to introduce finite elements. This book should be a valuable resource for students and practitioners in the fields of computer science and applied mathematics.

Table of contents

• Front Cover
• Numerical Methods for Partial Differential Equations
• Copyright Page
• Table of Contents
• Dedication
• Preface to second edition
• Preface to first edition
• Chapter 1. Fundamentals
• Chapter 2. Parabolic equations
• Chapter 3. Elliptic equations
• Chapter 4. Hyperbolic equations
• Chapter 5. Special topics
• Chapter 6. Weighted residuals and finite elements
• Author Index
• Subject Index