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.
Yi Tian (Thu,) studied this question.
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