In this article, we discuss a new 2-level implicit cubic spline method of order (2,4) for the numerical solution of 1D nonlinear parabolic equation -w xx +g(x,t,w,w x ,w t )=0, 00 subject to appropriate initial and Dirichlet boundary conditions prescribed on the boundary. Further, we discuss a new three-phase group explicit iteration procedure to solve nonlinear system of difference equations at each advanced time level as a numerical algorithm. The suggested three-phase iteration procedure is predicted to save the CPU-time as the common term is evaluated first at phase-I. The convergence analysis of the suggested iteration procedure is deliberated briefly. In application, we have solved a few benchmark problems including Burgers-Huxley, Burgers’ and singular parabolic equations. A comparison of the numerical results is carried out with the corresponding two-step Newton-AGE and Newton-SOR iteration procedures to demonstrate the usefulness of the purported iteration procedure in terms of CPU time and order of convergence.
Niranjan et al. (Thu,) studied this question.