Modified Compact Central Finite Difference Schemes For The Simulations Of Wave Equation At Any Wave Number

Hafiz Abdul Wajid, Hifza Iqbal

Keywords: Compact Finite Difference Schemes, Numerical dispersion, Numerical dissipation, Wave equation, High wave number, wave propagations, Vibrational analysis

Issue II, Volume I, Pages 67-85

In this paper, we present modified central finite difference (C.F.D.) schemes for solution of the

wave equation. The modified schemes (a) provide highly accurate solutions at nodes of the spatial

grid for all time steps; (b) preserve the compact stencil structure as of standard C.F.D. scheme and

higher order accuracy is achieved without implementation of new code; (c) offer highly accurate

solutions for low as well as high wave numbers without use of fine grid. Finally, in order to display

superiority of modified C.F.D. schemes numerical computations and graphs are presented for

applications such vibrating string and wave propagations compared with standard C.F.D. schemes.

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