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

In this paper, we present a finite element method involving Galerkin method with septic B-splines as basis functions to solve a general tenth order boundary value problem. The basis functions are redefined into a new set of basis functions which vanish on the boundary where the given set of boundary conditions are prescribed. The proposed method was applied to solve several examples of tenth 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 are compared with the exact solutions available in the literature.