General Software for Two-Dimensional Nonlinear Partial Differential Equations

In this paper we describe a software interface to solve time-dependent coupled systems of nonlinear partial differential equations (PDEs), which are defined over a two-dimensional rectangular rebqon. The software interface employs the method of lines technique whereby centered differencing with respect to the two spatial variables results in a system of time-dependent ordinary differential equations (ODEs), which can then be solved using one of the readily available modern ODE integrators. We also describe a routine to be used in conjunction with the interface for the efficient generation of the Jacobian matrix. Representative examples are given to demonstrate the use, validity, and capabihties of the accompanying algorithm.