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Local error and variable order Adams codes. (English) Zbl 0333.65037


MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
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References:

[1] Henrici, P., Discrete Variable Methods in Ordinary Differential Equations (1962), Wiley: Wiley New York · Zbl 0112.34901
[2] Krogh, F. T., vodq⧸svdq⧸dvdq-Variable order integrators for the numerical solution of ordinary differential equations, TU Doc. No. CP-2308, NPO-11643 (May 1969), Jet Propulsion Laboratory: Jet Propulsion Laboratory Pasadena, Calif
[3] Gear, C. W., Numerical Initial Value Problems in Ordinary Differential Equations (1971), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J · Zbl 0217.21701
[4] Piowtrowski, P., Stability, consistency and convergence of variable \(k\)-step methods for numerical integration of large systems of ordinary differential equations, (Conference on the Numerical Solution of Differential Equations. Conference on the Numerical Solution of Differential Equations, Lecture Notes in Mathematics, 109 (1969), Springer-Verlag: Springer-Verlag Berlin), 221-227 · Zbl 0191.16401
[5] Gear, C. W.; Watanabe, D. S., Stability and convergence of variable order multistep methods, Report No. 571 (1972), Dept. of Comp. Sci., Univ. of Ill: Dept. of Comp. Sci., Univ. of Ill Champaign-Urbana · Zbl 0294.65041
[6] Lefschetz, S., Differential Equations: Geometric Theory (1957), Interscience: Interscience New York · Zbl 0080.06401
[7] Gragg, W. B., Repeated extrapolation to the limit in the numerical solution of ordinary differential equations, Thesis (1964), UCLA
[8] Hull, T. E.; Creemer, A. L., Efficiency of predictor-corrector procedures, JACM, 10, 291-301 (1963) · Zbl 0115.34603
[9] Krogh, F. T., A variable step variable order multistep method for the numerical solution of ordinary differential equations, (Information Processing, 68 (1969), North-Holland: North-Holland Amsterdam), 194-199, Proceedings of the IFIP Congress 1968 · Zbl 0193.12701
[10] Hall, G., Stability analysis of predictor-corrector algorithms of Adams type, SIAM J. Numer. Anal., 11, 494-505 (1974) · Zbl 0286.65038
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