Analysis of a new numerical approach to solutions of heat conduction equations arising from heat diffusion

Abstract

In this work, a new numerical finite difference scheme with the aim of obtaining a new numerical scheme that will be used to solve for the solution of Partial Differential Equations (PDE) arising from heat conduction equation is developed. This is significant because in recent times there is a growing interest in literatures to obtain a continuous numerical method for solving PDE. The numerical accuracy of this new approach is also studied. Detailed numerical results have shown that the new method provides better results than the known explicit finite difference method by Schmidt. And in terms of stability, the new scheme has been able to clearly shown that it is more stable than the old Schmidt explicit method. There is no semi-discretization involved and no reduction of PDE to a system of ODEs in the new approach, but rather a system of algebraic equations is directly obtained. MATLAB software was
used to solve for the desired solutions and the results obtained has shown that the method is near exact solutions.