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Design and Implementation of a Software for Solving Wave Equations

Abstract:

Computational aspects of simulation and modeling in the solution of the Heaviside equation are presented. A second-order finite difference approximation scheme was used. The code was implemented in MATLAB and allowed to obtain the induced currents at the moment of an atmospheric discharge. This is a simple example that allows explaining how an algorithm implemented to solve the Heaviside equation which serves as a basis for solving wave equations that describe different physical phenomena and incorporates tools that allow performing more complete studies in the transient regime when studying atmospheric discharges in transmission lines. Improvements to previous works are introduced, which will contribute to developing more applications, since having more direct and interactive contact with the graphs of the transient regime will reinforce the knowledge about the physical phenomenon studied. In the numerical implementation, a finite difference second-order approximation scheme was used. To validate the code, convergence tests were performed, which allow us to conclude that the code is stable and convergent to the second order of approximation. It is demonstrated that the implemented code is general enough to be implemented in simulations of wave equations describing different physical systems.