On the convergence of Ritz and Galerkin's method in the case of certain nonconservative systems and using admissible coordinate functions

Abstract

For a certain nonconservative system with complicated dynamic boundary conditions, Ritz's method, or an extended version of Galerkin's method, respectively are applied to the calculation of the eigenvalue usingadmissible coordinate functions which satisfy the geometric boundary conditions but do not satisfy all of the dynamic boundary conditions. By showing the analogy of Ritz or the extended Galerkin method with the approximation of a certain integro-differential equation, means are obtained for proving the convergence of Ritz or the extended Galerkin method indirectly by proving the convergence of the analoguous approximate integro-differential equation.