Using a small algebraic manipulation system to solve differential and integral equations by variational and approximation techniques (Q1104710)

In the classical papers variational methods (Rayleigh-Ritz, Galerkin, least squares) for differential equations are usually illustrated on ``small'' examples, i.e. with a small number of basis functions. This notwithstanding the results usually prove to remarkably accurate due to the clever choice of the basis functions (and presumably also because bad results do not get published). In this paper the author shows how the computational work involved in these examples, such as integrations for the inner products and solving the linear equations, can be done by algebraic manipulation systems, with the aforementioned remarkable accuracy. By way of example, the author uses MUMATH running on a TRS80 Model 1 microcomputer.