Compact Schemes for the Simulations of Wave Propagations

In this paper, a general frame work for the development of compact schemesin particular for time harmonic wave equation is presented. The salient features thisframe work offers are (a) exact values of numerical solutions at the nodes of the spatialgrid irrespective of one or higher dimensions are obtained; (b) compact schemes pre-serves same stencil structure as that of the standard finite difference and finite elementschemes; (c) requirement of fine mesh size to enjoy desired level of accuracy is removedwhich is real trouble in the case of high wave numbers.