ABSTRACT

With emphasis on modern techniques, Numerical Methods for Differential Equations: A Computational Approach covers the development and application of methods for the numerical solution of ordinary differential equations. Some of the methods are extended to cover partial differential equations. All techniques covered in the text are on a program disk included with the book, and are written in Fortran 90. These programs are ideal for students, researchers, and practitioners because they allow for straightforward application of the numerical methods described in the text. The code is easily modified to solve new systems of equations.
Numerical Methods for Differential Equations: A Computational Approach also contains a reliable and inexpensive global error code for those interested in global error estimation. This is a valuable text for students, who will find the derivations of the numerical methods extremely helpful and the programs themselves easy to use. It is also an excellent reference and source of software for researchers and practitioners who need computer solutions to differential equations.

chapter 1|14 pages

Differential equations

chapter 2|16 pages

First ideas and single–step methods

chapter 3|15 pages

Error considerations

chapter 4|24 pages

Runge–Kutta methods

chapter 5|25 pages

Step–size control

chapter 6|19 pages

Dense output

chapter 7|18 pages

Stability and stiffness

chapter 8|13 pages

Multistep methods

chapter 9|17 pages

Multistep formulae from quadrature

chapter 10|21 pages

Stability of multistep methods

chapter 11|21 pages

Methods for Stiff systems

chapter 12|19 pages

Variable coefficient multistep methods

chapter 13|21 pages

Global error estimation

chapter 14|20 pages

Second order equations

chapter 15|17 pages

Partial differential equations