Effect of the Forcing Function values on the Numerical Simulation of General Second Order Linear Partial Differential Equation

Abstract

The second-order PDEs are used to model a wide variety of application problems and due to their indispensable usage the computational analysis of various aspects have worked out by researchers in the field. In this study, a computational analysis of the finite difference numerical solution of the general linear second-order PDE with constant coefficients is presented. The study’s objective was to examine the simultaneous effect of the varied size of the computational domain and the forcing function values on the numerical simulation. From the results, it is revealed that the forcing function affects the simulation patterns as long as the size of the domain is increased from 1 × 1 square unit to 2 × 2, 3 × 3, and 4 × 4. Also, the local node-wise solution values change considerably with the varied values of the forcing function. The effect of forcing function G values on the numerical solution is observed higher when G < 0 and is lower when G > 0. The outcomes of this research study are expected to provide ways to predict the simulations obtained by the general second-order PDE based on the varied domain size and the forcing function with constant coefficients of the PDE.