A variable mesh C-SPLAGE method of accuracy O(k2hl-1+khl+hl3) for 1D nonlinear parabolic equations

A new high accuracy two-level implicit cubic spline formulation for the solution of nonlinear parabolic equation uxx = ϕ(x, t, u, ux, ut) is presented. The strategy of the cubic spline alternating group explicit (C-SPLAGE) method is developed. The proposed C-SPLAGE method requires only 3-spatial grid points and applicable to singular problems. The convergence analysis of the proposed C-SPLAGE method is given. The obtained C-SPLAGE method is compared to the corresponding successive over relaxation (SOR) method both in terms of stability and performance.