Chikitkin, A. V.; Rogov, B. V. 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. Cited in 2 Documents 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 Keywords:bicompact scheme; semidiscrete scheme; sixth order of accuracy; method of lines Software:RODAS PDFBibTeX XMLCite \textit{A. V. Chikitkin} and \textit{B. V. Rogov}, Dokl. Math. 97, No. 1, 90--94 (2018; Zbl 1393.65008); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 478, No. 6, 631--636 (2018) Full Text: DOI References: [1] Colonius, T.; Lele, S. K., No article title, Prog. Aerosp. Sci., 40, 345-416, (2004) · doi:10.1016/j.paerosci.2004.09.001 [2] Ekaterinaris, J. A., No article title, Prog. Aerosp. Sci., 41, 192-300, (2005) · doi:10.1016/j.paerosci.2005.03.003 [3] Kurbatskii, K. A.; Mankbadi, R. R., No article title, Int. J. Comput. Fluid Dyn., 18, 533-546, (2004) · Zbl 1065.76595 · doi:10.1080/10618560410001673542 [4] A. I. Tolstykh, High Accuracy Compact and Multioperator Approximations for Partial Differential Equations (Nauka, Moscow, 2015) [in Russian]. [5] Tolstykh, A. I., No article title, Dokl. Math., 95, 136-139, (2017) · Zbl 1371.65100 · doi:10.1134/S1064562417020077 [6] Liu, X.; Zhang, S.; Zhang, H.; Shu, C.-W., No article title, J. Comput. Phys., 248, 235-256, (2013) · Zbl 1349.76504 · doi:10.1016/j.jcp.2013.04.014 [7] Xu, D.; Deng, X.; Chen, Y.; Wang, G.; Dong, Y., No article title, Adv. Appl. Math. Mech., 9, 1012-1034, (2017) · Zbl 1488.65564 · doi:10.4208/aamm.2016.m1477 [8] Chikitkin, A. V.; Rogov, B. V., No article title, Dokl. Math., 96, 480-485, (2017) · Zbl 1381.65077 · doi:10.1134/S1064562417050192 [9] E. Hairer and G. Wanner, Solving Ordinary Differential Equations, Vol. 2: Stiff and Differential-Algebraic Problems (Springer-Verlag, Berlin, 1996). · Zbl 0859.65067 · doi:10.1007/978-3-642-05221-7 [10] L. O. Jay, “Lobatto methods,” in Encyclopedia of Applied and Computational Mathematics (Springer, Berlin, 2015), pp. 817-826. · doi:10.1007/978-3-540-70529-1_123 [11] C. K. W. Tam, in Fourth Computational Aeroacoustics Workshop on Benchmark Problems, Svetlogorsk, 2004, NASA/CP-2004-212954. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.