STABLE ALGORITHM FOR THE WAVE EQUATION USING FINITE DIFFERENCE METHOD - Loumi, A (TWMS journal of applied and engineering mathematics, 2023)
The numerical solution of hyperbolic equations has shown instabilities in some studies (see [2]). In this paper, we use a trick to remedy the reasons for instabilities of particular example of hyperbolic equation, namely the wave equation. We propose a simple method based on the finite difference method and the projection on a manifold that conserves energy. Keywords: wave equation, projection, finite difference method. AMS Subject Classification: 33F05, 58J45, 65M22.