On stability and error bounds of an explicit in time higher-order vector compact scheme for the multidimensional wave and acoustic wave equations. (English) Zbl 07763848
Summary: We study a three-level explicit in time higher-order vector compact scheme, with additional \(n\) sought functions approximating second order non-mixed spatial derivatives of the solution, for an initial-boundary value problem for the \(n\)-dimensional wave equation and acoustic wave equation, with the variable speed of sound, \(n \geqslant 1\). We also approximate the solution at the first time level in a similar two-level manner, without using derivatives of the initial data as usual. For the first time, under the CFL-type conditions, new stability bounds in the standard and stronger mesh energy norms and the discrete energy conservation laws are presented, and the corresponding error bounds of the orders 4 and 3.5 are rigorously proved. Generalizations to the cases of the nonuniform meshes in space and time are described. Results of various numerical experiments are also included.
MSC:
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 35Lxx | Hyperbolic equations and hyperbolic systems |
| 65Nxx | Numerical methods for partial differential equations, boundary value problems |
Keywords:
wave equation; acoustic wave equation; explicit vector scheme; higher-order compact scheme; stability; error boundReferences:
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