## Solving ODEs with MATLAB

#### Book Description

This book is a text for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics. Prerequisites are a first course in the theory of ODEs and a survey course in numerical analysis, specific programming experience, preferably in MATLAB, and knowledge of elementary matrix theory. Professionals will also find that this valuable, concise reference contains reviews of technical issues and realistic and detailed examples. The programs for the models are supplied on the accompanying website and can serve as templates for solving other problems. Each chapter begins with a discussion of the “facts of life” of the situation, mainly using examples. Numerical methods for the trial are then developed, but only the most widely used methods. The treatment of each technique is brief and technical issues are minimized, but all the issues important in practice and for understanding the codes are discussed. The last part of each chapter is a tutorial showing how to solve problems using small but realistic examples.

#### Book Contents

1 Getting Started

Introduction
Existence, Uniqueness, and Well-Posedness
Standard Form
Control of the Error
Qualitative Properties

2 Initial Value Problems

Introduction
Numerical Methods for IVPs
One–Step Methods
Local Error Estimation
Runge–Kutta Methods
Explicit Runge–Kutta Formulas
Continuous Extensions
Methods with Memory
Adams Methods
BDF methods
Error Estimation and Change of Order
Continuous Extensions
Solving IVPs in Matlab
Event Location
ODEs Involving a Mass Matrix
Large Systems and the Method of Lines
Singularities

3. Boundary Value Problems

Introduction
Boundary Value Problems
Boundary Conditions
Boundary Conditions at Singular Points
Boundary Conditions at Infinity
Numerical Methods for BVPs
Solving BVPs in Matlab

4. Delay Differential Equations

Introduction
Delay Differential Equations
Numerical Methods for DDEs
Solving DDEs in Matlab
Other Kinds of DDEs and Software

#### Solving ODEs with MATLAB: Instructor’s Manual

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#### Author(s): L. F. Shampine, I. Gladwell, S. Thompson

Publisher: Cambridge University Press, Year: 2003

ISBN: 9780521824040

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