Optimal Finite Difference Schemes for Wave Equation

Abstract

In this research work the novel optimal central finite difference schemes for solving the transient wave equation, are developed and analyzed. The novel schemes (a) give exact value at the nodes of the grid, meaning that an exact solution is possible for the transient wave equation; (b) the key advantage is that they have the simple structure as that of the standard central finite difference schemes, so we just need to make few amendments in the standard codes, instead of writing the new codes altogether; (c) above all, the beauty lies in the fact that they do not require fine mesh size and works for any wave number, specially for high wave number. Finally, in order to display the actual power of the novel schemes, numerical computations and graphical representations for two model problems are added, by using both novel and standard central finite difference schemes, which support our theoretical results, by showing the superiority of the novel schemes compared to the standard schemes