A Look at Some Methods of Solving Partial Differential Equations and Eigenvalue Problems

Four techniques for the numerical solution of partial differential equations and eigenvalue problems were investigated. Typical problems considered were elliptic partial differential equations of the form U sub xx U sub yy fx,y, or U sub xx U sub yy lambda squared U O, where appropriate boundary conditions are specified so that the problem is self-adjoint. The four methods are relaxation, Galerkin, Rayleigh-Ritz, and dynamic programming combined with Stodolaa method, for eigenvalue problems. The results indicated that for eigenvalue problems relaxation or dynamic programming modified is to be preferred usually and for partial differential equations Galerkin or dynamic programming is preferred.