A new method for numerical solution of wave equation in hyperbolic model based on stochastic simulation

The objective of this paper is to examine the numerical solution of the wave equation. The wave equation is discretized by means of the implicit difference method, thereby yielding a large sparse system of linear algebraic equations (AU = b). Subsequently, the Jacobi over-relaxation iterative method is employed to transform it into the form of U = LU + f. The Monte Carlo method is employed to solve this system of equations. A particular instance substantiates the efficacy of this approach in approximating the exact solution with a reasonable degree of accuracy when solving the numerical solution of the wave equation, thus offering a novel methodology for the numerical solution of hyperbolic models.