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A class of self-starting methods for the numerical solution of \(y'' = f(x,y)\). (English) Zbl 0233.65042


MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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[1] J. C. Butcher,On Runge-Kutta Processes of High Order, J. Austral. Math. Soc., 4 (1964), 179–194. · Zbl 0244.65046
[2] P. C. Chakravarti and P. B. Worland,A New Self-Starting Sixth-Order Method for the Numerical Solution of the Equation y”=f(x,y), To appear. · Zbl 0316.65015
[3] L. Collatz,The Numerical Treatment of Differential Equations, Springer-Verlag, Berlin, 1960. · Zbl 0086.32601
[4] J. T. Day,A Runge-Kutta Method for the Numerical Integration of the Differential Equation y”=f(x,y), ZAMM, 45 (1971), 354–356. · Zbl 0136.12804
[5] R. de Vogelaere,A Method for the Numerical Integration of Differential Equations of Second Order Without Explicit First Derivatives, J. Res. N. B. S., 54 (1955), 119–125. · Zbl 0068.10302
[6] P. Henrici,Discrete Variable Methods in Ordinary Differential Equations, John Wiley and Sons, New York, 1969. · Zbl 0112.34901
[7] W. E. Milne,Numerical Solution of Differential Equations, John Wiley, New York, 1953. · Zbl 0050.12202
[8] R. E. Scraton,The Numerical Solution of Second Order Differential Equations Not Containing the First Derivative Explicitly, Computer Journal, 6 (1964), 368–370. · Zbl 0119.12303
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