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Extrapolation methods for dynamic partial differential equations. (English) Zbl 0425.65049


MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65B05 Extrapolation to the limit, deferred corrections
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations

Citations:

Zbl 0135.378
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Full Text: DOI EuDML

References:

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[2] Bulirsch, R., Stoer, J.: Numerical treatment of ordinary differential equations by extrapolation methods. Numer. Math.8, 1-13 (1966) · Zbl 0135.37901 · doi:10.1007/BF02165234
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[4] Cheng, S.I.: Numerical integration of Navier-Stokes equation. AIAA 8th Aerospace Sciences Meeting, New York, 1970
[5] Gary, J.M.: On the optimal time step and computational efficiency of difference schemes for PDEs. J. Computational Phys.16, 298-303 (1974) · Zbl 0293.65070 · doi:10.1016/0021-9991(74)90097-7
[6] Gary, J.M.: Comparison of some fourth order difference schemes for hyperbolic problems. Proc. AICA Int. Symp. Comp. Math. for PDE. (R. Vichnevetsky, ed.), pp. 14-16, 1975 · Zbl 0315.65053
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[8] Gragg, W.B.: On extrapolation algorithm for ordinary initial value problems. SIAM J. Numer. Anal.2, 384-403 (1965) · Zbl 0135.37803
[9] Israeli, M., Gottlieb, D.: On the stability of theN cycle scheme of Lorenz. Mon. Wea. Rev.102, 254-256 (1974) · doi:10.1175/1520-0493(1974)102<0254:OTSOTC>2.0.CO;2
[10] Kreiss, H.O., Oliger, J.: Comparison of accurate methods for the integration of hyperbolic equations. Tellus24, 199-215 (1972) · doi:10.1111/j.2153-3490.1972.tb01547.x
[11] Kreiss, H.O., Oliger, J.: Methods for the approximate solution of time dependent problems. GARP Publication Series, No. 10 (1973)
[12] Lapidus, L., Seinfeld, J.H.: Numerical solution of ordinary differential equations. New York: Academic Press 1971 · Zbl 0217.21601
[13] Lui, H.C.: A class of unconditionally stable second order implicit schemes for hyperbolic and parabolic equations. To appear
[14] Oliger, J.: Fourth order difference methods for the initial boundary-value problem for hyperbolic equations. Math. Comput.28, 15-26 (1974) · Zbl 0284.65074 · doi:10.1090/S0025-5718-1974-0359344-7
[15] Orszag, S.A.: Numerical simulation of incompressible flows within simple boundaries: Accuracy. J. Fluid Mech.49, 75-111 (1971) · Zbl 0229.76029 · doi:10.1017/S0022112071001940
[16] Orszag, S.A., Israeli, M.: Numerical simulation of viscous incompressible flows. Ann. Rev. Fluid Mech.6, 281-318 (1974) · Zbl 0295.76016 · doi:10.1146/annurev.fl.06.010174.001433
[17] Richtmyer, R.D., Morton, K.W.: Difference methods for initial value problems, 2nd ed. New York: Interscience 1967 · Zbl 0155.47502
[18] Skollermo, G.: Error analysis for the mixed initial boundary value problem for hyperbolic equations. Uppsala Dept. Comp. Sci., Report No. 63, 1975
[19] Smith, R.R., McCall, D.: Algorithm 392-system of hyperbolic P.D.E. Comm. ACM13, 567-570 (1970) · doi:10.1145/362736.362755
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[22] Turkel, E., Abarbanel, S., Gottlieb, D.: Multidimensional difference schemes with fourth order accuracy. J. Computational Phys.21, 85-113 (1976) · Zbl 0328.65045 · doi:10.1016/0021-9991(76)90021-8
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