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A First Course in the Numerical Analysis of Differential Equations, Second Edition

by Arieh Iserles

2009 (480 pages)

ISBN:9780521734905

Featuring copious illustrations and structured exercises, this valuable introductory text presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations.

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A First Course in the Numerical Analysis of Differential Equations, Second Edition
Preface to the Second Edition
Preface to the First Edition
Flowchart of Contents
Part I - Ordinary Differential Equations
Chapter 1	-	Euler’s Method and Beyond
Chapter 2	-	Multistep Methods
Chapter 3	-	Runge–Kutta Methods
Chapter 4	-	Stiff Equations
Chapter 5	-	Geometric Numerical Integration
Chapter 6	-	Error Control
Chapter 7	-	Nonlinear Algebraic Systems
Part II - The Poisson Equation
Chapter 8	-	Finite Difference Schemes
Chapter 9	-	The Finite Element Method
Chapter 10	-	Spectral Methods
Chapter 11	-	Gaussian Elimination for Sparse Linear Equations
Chapter 12	-	Classical Iterative Methods for Sparse Linear Equations
Chapter 13	-	Multigrid Techniques
Chapter 14	-	Conjugate Gradients
Chapter 15	-	Fast Poisson solvers
Part III - Partial Differential Equations of Evolution
Chapter 16	-	The Diffusion Equation
Chapter 17	-	Hyperbolic Equations
Appendix A	-	Bluffer’s Guide to Useful Mathematics