Convergence and stability criteria for numerical solutions of partial differential equations in science and engineering

Abstract

This paper explores the computational aspects of simulation and modeling applied to the solution of the Heaviside equation, considering the relevance of the stability and convergence of the solutions. For this purpose, a second-order finite difference scheme was implemented as the primary approach for studying atmospheric discharges (ATDI). The programming language used was Matlab, which facilitated calculating the induced currents in the study scenario. The centered, forward, and backward finite difference approaches were considered for the numerical implementation. System validation tests were performed to demonstrate the effectiveness of the design and convergence to the second order with the centered difference approach.