High Accurate Solver for Heat Equation using Modified Equation Approach

A new smaller bound has been proposed in this paper on the diffusion number for the heat equation using the concept of modified partial differential equations (MPDE). By choosing a suitable diffusion number for heat equation, a high order accurate numerical solution can be generated. For the computational stability, a truncated modified equation has been used to understand the insight of dispersion and dissipative error terms. Computational results have been shown for the heat and Burger's equations and also compared with the series solution.