Numerical Solution of Linear Parabolic Equation With Rational Coefficients

Abstract

In this paper, we present explicit scheme for solving rational coefficient (which depends only on space variable) parabolic equation. The explicit scheme is required some restriction on step size ratio k/h^2, →0 in stability, where k and h are step sizes for space and time respectively. In this paper, we will present the explicit scheme is sable without restriction on the step size ratio k/h^2. We also show the scheme converge to true solution under some conditions on coefficient.