Collocation Method for Fifth Order Boundary Value Problems by Using Quintic B-splines

Abstract

A finite element method involving collocation method with Quintic B-splines as basis functions has been developed to solve fifth order boundary value problems. The fifth order derivative for the dependent variable is approximated by the finite differences. The basis functions are redefined into a new set of basis functions which in number match with the number of collocated points selected in the space variable domain. The proposed method is tested on three linear and two non-linear boundary value problems. The solution to a nonlinear problem has been obtained as the limit of a sequence of solutions of linear problems generated by the quasilinearization technique. Numerical results obtained by the present method are in good agreement with the exact solutions available in the literature.