In this paper, we present a finite element method involving Galerkin method with quintic B-splines as basis functions to solve a general eighth order two point boundary value problem.The basis functions are redefined into a new set of basis functions which vanish on the boundary where Dirichlet type of boundary conditions, Neumann boundary conditions, second order derivative boundary conditions and third order derivative type of boundary conditions are prescribed. The proposed method was applied to solve several examples of the eighth 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 exact solutions available in the literature.

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A finite element method involving Galerkin method with quartic B-splines as basis functions has been developed to solve a general fifth order boundary value problem. The basis functions are redefined into a new set of basis functions which vanish on the boundary where Dirichlet type of boundary conditions and Neumann boundary conditions are prescribed. The proposed method was applied to solve several examples of fifth order linear and nonlinear boundary value problems. The solution of a non-linear 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.

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