In this paper, we develop a collocation method based on cubic B-spline to the solution of nonlinear parabolic equation "uxx = a(x, t)ut +f (x, t, u, ux) subject to appropriate initial, and Dirichlet boundary conditions, where " > 0 is a small constant. We developed a new two-level three-point scheme of order O(k2 + h2). The convergence analysis of the method is proved. Numerical results are given to illustrate the efficiency of our method computationally.
