SFOPDES: A Stepwise First Order Partial Differential Equations Solver with a Computer Algebra System

Abstract

Partial Differential Equations (PDE) appear in multiple Physic and Engineering applications. Normally, when modeling an application, the use of well-known and already solved PDE is considered. But what happens if a new PDE is used? Solving a new PDE is not an easy task. In this paper, we use a Computer Algebra System (Cas) in order to find the solution of PDE of first order. Specifically, we deal with Pfaff Equations, Quasilinear PDE and general first order PDE (using Lagrange–Charpit Method). To solve these PDE, we combine the power of a Cas with the flexibility of programming with it. Furthermore, the developed programs do not only provide the final result but also display all the intermediate steps which lead to find the solution of the PDE. This way, we introduce SFOPDES, a new Stepwise First Order PDE Solver which serves as a tutorial showing, step by step, the way to deal with PDE.