FINITE ELEMENT APPROACH TO SOLVE SEVENTH ORDER BOUNDARY VALUE PROBLEMS USING QUINTIC B-SPLINES

Abstract

A finite element method involving Galerkin method with quintic B-splines as basis functions has been been solved the seventh order boundary value problem with boundary conditions. The basis functions are redefined into a new set of basis functions which vanish at the boundary where Dirichlet type of boundary conditions and Neumann boundary conditions, second derivative boundary conditions are prescribed. The proposed method was applied to solve several examples of sixth order linear and nonlinear boundary value problems. The solution of a nonlinear boundary value problem has been obtained as the limit of a sequence of solution of linear boundary value problems generated by quasilinearization technique. The obtained numerical results were found to be in good agreement with exact solutions available in the literature.