Numerical investigation of the heat flow problem using rayleigh ritz, stws and runge-kutta methods based on various means

In this article numerical investigation of an interesting heat flow problem is discussed using Rayleigh Ritz, single-term Walsh series (STWS) method and Runge-Kutta (RK) method based on various means. The results (approximate solutions) obtained very accurate using the above said methods are compared with the exact solution of that problem. It is found that the solution obtained using RKCeM (Runge-Kutta Centroidal Mean) is closer to the exact solution of the heat flow problem. The high accuracy and the wide applicability of RKCeM approach will be demonstrated with numerical example. Solution graphs for discrete exact solutions are presented in a graphical form to show the efficiency of the RKCeM. The results obtained show that RKCeM is more useful for solving the heat flow problem and the solution can be obtained for any length of time.