A meshless finite difference scheme applied to the numerical solution of wave equation in highly irregular space regions

Even when the wave equation is a classical problem to solve in courses about hyperbolic partial differential equations, the numerical solution for this equation in irregular regions has been little studied. This is because of all the problems that could arise when solving the second-order derivative in time.This paper presents a generalized finite difference scheme applied to the numerical solution of the wave equation, solved on clouds of points for highly irregular domains. The implementation over clouds of points allows this scheme to compute satisfactory results, with minor quadratic errors, over highly irregular regions, as discussed in the present manuscript. Also, the numerical results show the accuracy obtained with a straightforward and low-cost implementation.