Exact solution and its pertinent numerical methodology for wave equation subject to local boundary or nonlocal integral conditions

Abstract

In this paper, we propose exact solution as well as an efficacious numerical method for the wave equation subject to local boundary or nonlocal integral conservation conditions. This exact solution and numerical method were developed based on the essential features of the equation system, which were revealed in the characteristic analyses. The existence, uniqueness, and smooth variation owing to the initial conditions were simultaneously verified by the explicit expression of the exact solution. Discrepancies in the numerical method for solution propagation within the computational domain were effectively eliminated using the proposed computational particle movement strategy. The solution error stems from the interpolation procedure used to comply with the boundary or integral conservation conditions. Solution evolution in the computational domain can be faithfully simulated by the proposed method without incurring further numerical errors. Therefore, based on the computational results for several test problems, the method is justified to be a highly effective simulation tool for the wave equation system.