Date of Publication :30th September 2021
Abstract: An explicit method is computationally simple but it is only valid for 0 < k/h^2 = r?0.5. Crank and Nicolson (1947) proposed and used an implicit method that is valid for all finite values of r. We proposed a modified Implicit method for solving one dimensional heat equation with initial and boundary conditions and this method is valid for 0 < r ? 1.0.. Test examples solved using modified implicit method gave good approximations to exact solutions of parabolic partial differential equations. We also observed that percentage errors computed in test examples which are solved by our method are less than those percentage errors in respective test examples solved by crank Nicolson Implicit method
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