Software for Nonlinear Partial Differential Equations

Abstract

The numerical solution of physically realistic nonlinear partial differential equations (PDEs) is a complicated and highly problem dependent process which usually requires the scientist to undertake the difficult and time consuming task of developing his own computer program to solve his problem. This paper presents a useful and reliable software interface which can ehminate much of the expensive and time consuming effort involved in the solution of nonlinear PDEs. The software interface provides centered differencing in the spatial variable for time dependent nonlinear PDEs, giving a semidlscrete system of nonhnear ordinary differential equations (ODEs) which are then solved using one of the recently developed robust ODE integrators. Besides being portable, efficient, and easy to use, the software interface along with an ODE integrator will discretize the problem, select the time step and order, solve the nonlinear equations (checking for convergence, etc.), and maintain a user specified time integration accuracy, all automatically and reliably.