Abstract
A new high accuracy two-level implicit cubic spline formulation for the solution of nonlinear parabolic equation u xx = ϕ( x, t, u, u x , u t ) 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.
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