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In (2), we have presented some new algorithms for solving the linear variable coefficients parabolic differential equations. The proposed scheme is stable without any restriction to step-sizes of space and time. The scheme is required the condition of step size ratio k h2,→ 0 as k,h → 0 in the convergence, where k and h are step sizes for space and time respectively. In this paper, we will present the explicit unconditional stable scheme which has no restriction on the step size ratio k h2 in the convergence. We will also present analysis for the present scheme.

A STUDY ON UNCONDITIONALLY STABLE EXPLICIT DIFFERENCE SCHEMES FOR THE VARIABLE COEFFICIENTS PARABOLIC DIFFERENTIAL EQUATION