Galerkin's method and the variational procedure

Galerkin's method and the variational procedure, when applied to most practical problems in electromagnetics, lead to matrix equations of the same form. Variational procedures for self-adjoint and nonself-adjoint operators also result in the same form of matrix equations for a large subclass of problems. However, the three cases may yield different matrix equations in general. This paper examines the subclass of problems for which these methods result in the same matrix equation and provides systematic ways for classification of problems for which two or all three of the cases lead to the same matrix equation. It also describes properties of the coefficient matrix in the matrix equation.