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A Compact 4th-Order Scheme for the General Acoustic Wave Equation
Lobachevskii Journal of Mathematics. 2026. Vol. 47. No. 5. P. 2446–2460.
We deal with the general multidimensional acoustic wave equation, where both the speed of sound and density of a medium are variable, that is physically relevant. For the first time, we develop a new compact scheme for this equation which is three-level in time, three-point in each spatial direction and has the fourth truncation order $\mathcal{O}(|h|^4+h_t^4)$. In addition, the scheme is semi-explicit in time and easily implementable. It non-trivially generalizes a semi-explicit vector compact scheme constructed and studied recently in the much simpler case of the constant density. Although other high-order numerical methods for the general acoustic wave equation were known, the construction of a compact high-order scheme remained an unsolved problem for a long time. Results of computations confirm the high precision of the scheme and its fourth error order not only in the mesh $C$ norm but in the mesh $C^1$ norm as well that is of value in applications.
Keywords: practical error analysisacoustic wave equationcompact fourth-order schemevariable speed of sound and densitysemi-explicit three-level scheme
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Smooth principal bundles whose total spaces and bases are time oriented Lorentzian manifolds and whose projections are Lorentzian submersions preserving time orientations are studied. Previously, the authors showed that the chronologicity, causality, and stable causality always lift from the base to the space of a Lorentzian bundle. For strong causality and global hyperbolicity, this holds ...
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