Efficient Solution of Burgers’, Modified Burgers’ and KdV–Burgers’ Equations Using B-Spline Approximation Functions

This paper discusses the application of orthogonal collocation on finite elements (OCFE) method using quadratic and cubic B-spline basis functions partial differential equations. Collocation is performed at Gaussian points to obtain an optimal solution, hence name collocation. The used solve various cases Burgers’ equations, including modified equation. KdV–Burgers’ equation considered as a test case for OCFE splines. results compare favourably with existing results. stability convergence are also given consideration. unconditionally stable second-order accurate in time space.