Solution of heat equation with variable coefficient using derive

Abstract

In this paper, the method of approximating solutions of partial differential equations with variable coefficients is studied. This is done by considering heat flow through a one-dimensional model with variable cross-sections. Two cases are considered. The first one involves quadratic approximation of the variable coefficient by direct integration. This case is studied using a conic domain. The second case approximates the variable coefficient quadratically and by step functions. The solution of the problem in each case is expressed using Green's function, and the results are compared. By the suitable use of a computer algebra system (CAS) all of these ideas can easily enough be introduced at the advanced undergraduate level