SAMS Subject Classification Number: 23

This paper discussed the application of orthogonal collocation finite element method using a third order B-spline basis functions to ordinary and partial differential equations. Collocation was done at Gaussian points to get optimal solution, hence the name orthogonal. The method is used to solve various particular solutions of Burgers’ equation and the results compared favourably with existing results. The stability and convergence of the method are also given consideration. Our results show that it is unconditionally stable, second order accurate in time and space and performed better than existing results based on other quadratic splines in literature.