Galerkin Residual Correction for Fourth Order BVP

This article uses residual correction procedure for improving the Galerkin approximate solutions to higher order boundary value problem (BVP). The residual function of a differential equation is found from the approximate solution of a BVP and setting it as nonhomogeneous term we get the error differential equation. We exploit Bernstein and Bernoulli polynomials as basis functions to solve the two differential equations, namely, original and its error equations, by Galerkin technique subject to the corresponding boundary conditions. Linear and nonlinear problems of fourth order BVPs are considered to verify the proposed method. The resulting numerical solutions are compared with the analytic solutions as well as the results of other approaches those have been reported in the literature. This method is also applied to sixth order BVPs. The comparison reveals that the current procedure is more accurate.