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How to increase the order to get minimal-error algorithms for systems of ODE. (English) Zbl 0527.65055


MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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References:

[1] Babenko, K.I.: Theoretical foundations and construction of computational algorithms for the problems of mathematical physics, Moscow, 1979 (in Russian)
[2] Gear, C.W.: Numerical initial value problems in ordinary differential equations. Englewood Cliffs: Prentice Hall 1971 · Zbl 1145.65316
[3] Hall, G., Watt, J.M.: Modern numerical methods for ordinary differential equations. Oxford: Clarendon Press 1976 · Zbl 0348.65064
[4] Henrici, P.: Discrete variable methods in ordinary differential equations. New York-London: J. Wiley and Sons 1962 · Zbl 0112.34901
[5] Kacewicz, B.Z.: On the optimal error of algorithms for solving a scalar autonomous ODE. BIT22, 503-518 (1982) · Zbl 0501.65037 · doi:10.1007/BF01934413
[6] Kacewicz, B.Z.: Optimality of Euler-integral information for solving a scalar autonomous ODE. BIT23, 217-230 (1983) · Zbl 0516.65055 · doi:10.1007/BF02218442
[7] Lambert, J.D.: The initial value problem for ordinary differential equations. In: The state of the art in numerical analysis (D.A. Jacobs, eds.). London-New York: Academic Press 1977
[8] Traub, J.F., Wo?niakowski, H.: A general theory of optimal algorithms. New York-London: Academic Press 1980
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