Numerical Solution of Eighth Order Boundary Value Problems by Galerkin Method with Septic B-splines

Abstract

A finite element method involving Galerkin method with septic B-splines as basis functions has been solved the eighth order boundary value problems The basis functions are redefined into a new set of basis functions which vanish at the boundary where all types of boundary conditions are prescribed. The proposed method was applied to solve several examples of eighth order linear and nonlinear boundary value problems. To test the efficiency of the proposed method, obtained numerical results are compared with exact solutions available in the literature.