文档介绍：Ordinary and Partial Differential
Equation Routines in C, C++,
Fortran, Java®, Maple®, and MATLAB®
. Lee and . Schiesser
CHAPMAN & HALL/CRC
A CRC pany
Boca Raton London New York Washington, .
Copyright 2004 by Chapman & Hall/CRC
Preface
Initial value ordinary differential equations (ODEs) and partial differential
equations (PDEs) are among the most widely used forms of mathematics in
science and engineering. However, insights from ODE/PDE-based models
are realized only when solutions to the equations are produced with accept-
able accuracy and with reasonable effort.
Most ODE/PDE models plicated enough (., sets of simultane-
ous nonlinear equations) to preclude analytical methods of solution; instead,
numerical methods must be used, which is the central topic of this book.
The calculation of a numerical solution usually requires that well-
established numerical integration algorithms are implemented in quality li-
brary routines. The library routines in turn can be coded (programmed) in a
variety of programming languages. Typically, for a scientist or engineer with
an ODE/PDE- based mathematical model, finding routines written in a famil-
iar language can be a demanding requirement, and perhaps even impossible
(if such routines do not exist).
The purpose of this book, therefore, is to provide a set of ODE/PDE in-
tegration routines written in six widely accepted and used languages. Our
intention is to facilitate ODE/PDE-based analysis by using the library rou-
tines pute reliable numerical solutions to the ODE/PDE system of
interest.
However, the integration of ODE/PDEs is a large subject, and to keep this
discussion to reasonable length, we have limited the selection of algorithms
and the associated routines. Specifically, we concentrate on explicit (nonstiff)
Runge Kutta (RK) embedded pairs. Within this setting, we have provided
integrators that are both fixed step and variable step; the latt