On Properties of a Semi-Explicit Vector Compact Scheme for the Acoustic Wave Equation
PDF (Russian)

Keywords

acoustic wave equation
semi-explicit three-level vector scheme
compact scheme of the 4-th order of accuracy
conditional stability
error bound

How to Cite

1.
Zlotnik A.A., Lomonosov T.A. On Properties of a Semi-Explicit Vector Compact Scheme for the Acoustic Wave Equation // Russian Journal of Cybernetics. 2024. Vol. 5, № 3. P. 6-12. DOI: 10.51790/2712-9942-2024-5-3-01.

Abstract

we numerically solved an initial-boundary value problem for the n-dimensional acoustic wave equation (n ⩾ 1) with variable sound speed and nonhomogeneous Dirichlet boundary conditions. We studied a non-standard, three-level, semi-explicit compact scheme. The scheme uses three points per spatial direction and exploits n auxiliary functions to approximate second-order non-mixed spatial derivatives. At the first time level, we applied a two-level scheme without using data derivatives. The scheme involves solving tridiagonal matrix systems in all n spatial directions. We proved theorems on conditional stability and 4th-order error bounds. Our 3D experiments confirmed 4th-order accuracy with minimal error, even on coarse meshes.

https://doi.org/10.51790/2712-9942-2024-5-3-01
PDF (Russian)

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