Numerical Methods for Ordinary Differential Equations

ISBN 10: 9065621563 / ISBN 13: 9789065621566

Published by VSSD, 2009

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Synopsis:

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

From the Back Cover: 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

Bibliographic Details

Title: Numerical Methods for Ordinary Differential ...
Publisher: VSSD
Publication Date: 2009
Binding: paperback
Condition: Very Good