Keywords
semi-explicit three-level vector scheme
compact scheme of the 4-th order of accuracy
conditional stability
error bound
How to Cite
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.
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