Harten, Ami; Engquist, Bjorn; Osher, Stanley; Chakravarthy, Sukumar Uniformly high order accurate essentially non-oscillatory schemes. III. (English) Zbl 0652.65067 J. Comput. Phys. 71, 231-303 (1987). [For part I cf. the first and the third author, SIAM J. Numer. Anal. 24, 279-309 (1987; Zbl 0627.65102).] The authors continue the studying of essentially nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws. New schemes which generalize Godunov’s scheme and its second-order extension are constructed. Algorithms for numerical solution of the Euler equations of gas dynamics are described and some numerical experiments are discussed. Reviewer: P.I.Ialamov Cited in 18 ReviewsCited in 804 Documents MSC: 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35L65 Hyperbolic conservation laws Keywords:numerical examples; nonoscillatory shock capturing methods; hyperbolic conservation laws; Godunov’s scheme; Algorithms; Euler equations; gas dynamics PDF BibTeX XML Cite \textit{A. Harten} et al., J. Comput. Phys. 71, 231--303 (1987; Zbl 0652.65067) Full Text: DOI References: [1] \scM. Ben-Artzi and J. Falcowitz, SIAM J. Sci. Comput., in press. [2] Chakravarthy, S.R.; Harten, A.; Osher, S., Essentially non-oscillatory shock-capturing schemes of arbitrarily high accuracy, Aiaa 86-0339, (1986), Reno, NA [3] Chorin, A.J., J. comput. phys., 22, 517, (1976) [4] Colella, P.; Woodward, P.R., J. comput. phys., 54, 174, (1984) [5] Godunov, S.K., Mat. sb., 47, 271, (1959) [6] Harabetian, E., A convergent series expansion for hyperbolic systems of conservation laws, NASA contractor report 172557, ICASE report no. 85-13, (1985), (unpublished) [7] Harten, A., Math. comp., 32, 363, (1978) [8] Harten, A., J. comput. phys., 49, 151, (1983) [9] Harten, A., J. comput. phys., 49, 357, (1983) [10] Harten, A., Sinum, 21, 1, (1984) [11] Harten, A., On high-order accurate interpolation for non-oscillatory shock capturing schemes, (), (unpublished) · Zbl 0606.76084 [12] Harten, A., Preliminary results on the extension of ENO schemes to two-dimensional problems, (), (in preparation) · Zbl 0626.65082 [13] Harten, A.; Hyman, J.M., J. comput. phys., 50, 235, (1983) [14] Harten, A.; Lax, P.D.; van Leer, B., SIAM rev., 25, 35, (1983) [15] SINUM, in press. [16] \scA. Harten, B. Engquist S. Osher, and S. R. Chakravarthy, Uniformly high-order accurate non-oscillatory schemes, II, in preparation. · Zbl 0866.65058 [17] Harten, A.; Osher, S.; Engquist, B.; Chakravarthy, S.R., J. appl. num. math., 2, 347, (1986) [18] Lax, P.D., Comm. pure appl. math., 7, 159, (1954) [19] Lax, P.D., Hyperbolic systems of conservation laws and the mathematical theory of shock waves, () · Zbl 0108.28203 [20] Lax, P.D.; Wendroff, B., Commun. pure appl. math., 13, 217, (1960) [21] Lax, P.D.; Wendroff, B., Commun. pure appl. math., 17, 381, (1964) [22] van Leer, B., J. comput. phys., 32, 101, (1979) [23] Osher, S., Sinum, 21, 217, (1984) [24] \scS. Osher and E. Tadmor, Math. Comp., in press. [25] Roe, P.L., J. comput. phys., 43, 357, (1981) [26] Roe, P.L., Some contributions to the modeling of discontinuous flows, () · Zbl 0741.65077 [27] Sever Mock, M., Order of dissipation near rarefaction centers, (), 395 [28] Sod, G.A., J. comput. phys., 27, 1, (1978) [29] Strang, G., Sinum, 5, 506, (1968) [30] Sweby, P.K., Sinum, 21, 995, (1984) [31] Woodward, P.; Collella, P., J. comput. phys., 54, 115, (1984) [32] Wu, Xiong-Hau; Zhu, You-Lan, A scheme of the singularity-separating method for the nonconvex problem, (), (unpublished) · Zbl 0584.76111 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.