ZZ Fourth Order Compact BVM for the Equation of Lateral Heat Loss

Zain Ul Abadin Zafar, M.O. Ahmad, A. Pervaiz, Nazir Ahmad


In this paper we combine the boundary value method (for discretizing the temporal variable) and finite difference scheme (for discretizing the spatial variables) to numerically solve the Equation of Lateral Heat Loss. This equation is also used in Probability, Stochastic processes and Brownian movements of gases. We first employ a fourth order compact scheme to discretize the spatial derivatives, and then a linear system of ordinary differential equations is obtained. Then we apply a fourth order scheme of boundary value method to approach this system. After this we use the central difference scheme for the temporal variables. Therefore, this scheme can achieve fourth order accuracy for spatial variables. For stability analysis we have used the Von Neumann Stability. Numerical results are presented to illustrate the accuracy and efficiency of this compact difference scheme, compared with finite difference scheme.

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