A NUMERICAL COMPARISON OF ALTERNATIVE GALERKIN METHODS FOR EIGENVALUE ESTIMATION

This paper provides a concise and unified comparison of four distinct variations of Galerkin's method. The four Galerkin variations are the explicit (traditional), implicit, quadratic implicit, and diagonalized-implicit Galerkin methods. Results indicate that the explicit Galerkin method is superior to all implicit formulations. Among the implicit methods, the quadratic implicit and diagonalized-implicit perform equivalently and are significantly better than the standard implicit method. The explicit method is recommended in all the cases except those in which the number of trial functions is so large that numerical conditioning affects the eigenvalue estimate. In this case, the diagonalized-implicit method is recommended.