Compact Schemes for the Simulations of Wave Propagations


  • Hafiz Abdul Wajid
  • Muhammad Abid
  • Ayesha Sohail



In this paper, a general frame work for the development of compact schemes in particular for time harmonic wave equation is presented. The salient features this frame work offers are (a) exact values of numerical solutions at the nodes of the spatial grid irrespective of one or higher dimensions are obtained; (b) compact schemes preserves same stencil structure as that of the standard finite difference and finite element schemes; (c) requirement of fine mesh size to enjoy desired level of accuracy is removed which is real trouble in the case of high wave numbers. Keywords: Time harmonic wave equation; High wave number; Compact schemes; Wave propagations. 2010 Mathematics Subject Classification: 65N15, 65N30, 65N35..