Sextic B-Spline Collocation Method for Eighth Order Boundary Value Problems

A finite element method involving collocation method with sextic B-splines as basis functions has been developed to solve eighth order boundary value problems. The sixth order, seventh order and eighth order derivatives for the dependent variable are approximated by the central differences of fifth order derivatives. 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 several linear and non linear boundary value problems. The solution of a non-linear boundary value problem has been obtained as the limit of a sequence of solutions of linear boundary value problems generated by quasilinearization technique. Numerical results obtained by the present method are in good agreement with the exact solutions available in the literature.