Software for Nonlinear Partial Differential Equations

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 software interface which can eliminate 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 semidiscrete system of nonlinear 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. Physically realistic examples are given to illustrate the use and capability of the software.

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