SYMBOLIC SOLUTION OF BOUNDARY VALUE PROBLEM VIA MATHEMATICA

Abstract

Symbolic computation has been applied to Runge-Kutta technique in order to solve a two-point boundary value problem. The unknown boundary values are considered as symbolic variables, therefore they will appear in a system of algebraic equations, after the integration of the ordinary differential equations. Then this algebraic equation system can be solved for the unknown initial values and substituted into the solution. Consequently, only one integration pass is enough to solve the problem instead of using an iteration technique like shooting method. This procedure is illustrated by solving the boundary value problem of the mechanical analysis of a liquid storage tank. Computations were carried out by the MATHEMATICA symbolic system.