A Direct Numerical Formulation of Galerkin’s Method for Nonlinear Lumped Systems

Abstract

Use of Galerkin’s method for the approximate analysis of nonlinear lumped systems is considered. A numerical procedure for finding Galerkin solutions of initial value problems is developed and illustrated by two examples. The approach employs Galerkin’s method formulated as a two-point boundary-value problem. While solving the two-point problem, a recursion algorithm is obtained; the algorithm is applied to the Galerkin integral directly, and therefore analytical integration of the weighted equation residuals and solution of specific algebraic equations are not required. The numerical formulation renders Galerkin’s method systematic, and it extends the utility of the method.