rkf45 is a Maxima function for solving initial value problems with adaptive step size and error control. It implements the Runge-Kutta-Fehlberg fourth-fifth-order method. The user doesn't need to care about the integration step, as it is selected by the algorithm itself, so that the error in solution returned should be smaller that a user-specified absolute tolerance. rkf45 should be able to solve any initial value problem efficiently, provided it is not very stiff. Note, however, that rkf45 is an explicit method, and, as such, it is not specifically designed for solving stiff differential equations. This means that, in case of very stiff problems, rkf45 will probably need much more iterations than usual to solve the problem.
Note: Since version 5.27, rkf45 is included in Maxima, so you don't need to download anything from here anymore. You can use rkf45 in your Maxima sessions by just typing load(rkf45);On Linux, all the above files, including the extensive documentation, are in the folder /usr/share/maxima/<version>/share/contrib/rkf45 (and a similar folder for those still insisting using Windows.) |