Document Zbl 0345.65049

Hybrid difference methods for the initial boundary-value problem for hyperbolic equations. (English) Zbl 0345.65049

Math. Comput. 30, 724-738 (1976).

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MSC:

65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
35L45	Initial value problems for first-order hyperbolic systems
35L50	Initial-boundary value problems for first-order hyperbolic systems

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[1]	Gerald Browning, Heinz-Otto Kreiss, and Joseph Oliger, Mesh refinement, Math. Comp. 27 (1973), 29 – 39. · Zbl 0256.65041
[2]	Melvyn Ciment, Stable difference schemes with uneven mesh spacings, Math. Comp. 25 (1971), 219 – 227. · Zbl 0223.65051
[3]	Melvyn Ciment, Stable matching of difference schemes, SIAM J. Numer. Anal. 9 (1972), 695 – 701. · Zbl 0221.65158 · doi:10.1137/0709058
[4]	T. ELVIUS & A. SUNDSTRÖM, ”Computationally efficient schemes and boundary conditions for a fine-mesh barotropic model based on the shallow-water equations,” Tellus, v. 25, 1973, pp. 132-156.
[5]	B. FORNBERG, On High Order Approximations of Hyperbolic Partial Differential Equations by a Fourier Method, Report 39, Dept. of Computer Sciences, Uppsala University, 1972.
[6]	B. GUSTAFSSON, On the Convergence Rate for Difference Approximations to Mixed Initial Boundary Value Problems, Report 33, Dept. of Computer Sciences, Uppsala University, 1971.
[7]	Bertil Gustafsson, Heinz-Otto Kreiss, and Arne Sundström, Stability theory of difference approximations for mixed initial boundary value problems. II, Math. Comp. 26 (1972), 649 – 686. · Zbl 0293.65076
[8]	H.-O. Kreiss, Difference approximations for initial boundary-value problems, Proc. Roy. Soc. London Ser. A 323 (1971), 255 – 261. A discussion on numerical analysis of partial differential equations (1970). · Zbl 0231.65073 · doi:10.1098/rspa.1971.0101
[9]	Heinz-Otto Kreiss and Joseph Oliger, Comparison of accurate methods for the integration of hyperbolic equations, Tellus 24 (1972), 199 – 215 (English, with Russian summary).
[10]	Morris Marden, Geometry of polynomials, Second edition. Mathematical Surveys, No. 3, American Mathematical Society, Providence, R.I., 1966. · Zbl 0162.37101
[11]	Joseph Oliger, Fourth order difference methods for the initial boundary-value problem for hyperbolic equations, Math. Comp. 28 (1974), 15 – 25. · Zbl 0284.65074

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