Solution of Eighth-Order Boundary Value Problems by Petrov-Galerkin Method with Quintic and Sextic B-Splines

摘要

In this paper, quintic B-splines (QBS) as basis (test) functions and sextic B-splines (SBS) as weight functions have been used in Petrov-Galerkin method to solve an eighth-order boundary value problem. The approximate solution has been modified into a form which takes care of most of the given boundary conditions. The weight functions are modified into a new set which suits for the Petrov-Galerkin method. Some examples are tested for the illustration purpose of the present method.