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Optimized symmetric bicompact scheme of the sixth order of approximation with low dispersion for hyperbolic equations. (English. Russian original) Zbl 1393.65008

Dokl. Math. 97, No. 1, 90-94 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 478, No. 6, 631-636 (2018).
Summary: A dispersion analysis of semidiscrete schemes from the one-parameter family of symmetric bicompact schemes of the sixth order of accuracy in space is performed. In this family, a scheme is found that has the smallest maximum phase error in the entire range of wavelengths resolvable on an integer-node grid. The maximum phase error of this optimized scheme does not exceed one-hundredth of percent. A numerical example is presented that demonstrates the ability of the bicompact scheme to adequately simulate short wave propagation on coarse grids at long times.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35L60 First-order nonlinear hyperbolic equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations

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References:

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