Numerical methods for ordinary differential equations

Numerical Methods for Ordinary Differential Equations

A big advantage of numerical mathematics is that a numerical solution can be

obtained for problems, where an analytical solution does not exist. An additional

advantage is, that a numerical method only uses evaluation of standard functions and

the operations: addition, subtraction, multiplication and division. Because these are

just the operations a computer can perform, numerical mathematics and computers

form a perfect combination.

An analytical method gives the solution as a mathematical formula, which is an

advantage. From this we can gain insight in the behavior and the properties of the

solution, and with a numerical solution (that gives the function as a table) this is not

the case. On the other hand some form of visualization may be used to gain insight

in the behavior of the solution. To draw a graph of a function with a numerical method

is usually a more useful tool than to evaluate the analytical solution at a great number

of points.

In this book we discuss several numerical methods for solving ordinary differential

equations. We emphasize those aspects that play an important role in practical

problems. In this introductory text we confine ourselves to ordinary differential

equations with the exception of the last chapter in which we discuss the heat

equation, a parabolic partial differential equation. The techniques discussed in

the introductory chapters, for e.g. interpolation, numerical quadrature and the solution

of nonlinear equations, may also be used outside the context of differential equations.

They have been included to make the book self contained as far as the numerical

spects are concerned.

Contents: Preface | 1. Introduction | 2. Interpolation | 3. Numerical differentiation |

4. Nonlinear equations | 5. Numerical quadrature | 6. Numerical time integration of

initial value problems | 7. The finite difference method for boundary value problems |

8. The instationary equation | Literature | Index

Published by VSSD

URL about this book: http://www.vssd.nl/hlf/a026.htm