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References
Henrici, P.: Discrete variable methods in ordinary differential equations. New York: J. Wiley & Sons, 1962.
Babuška, I., M. Práger, and E. Vitásek: Numerical processes in differential equations. London: J. Wiley & Sons, 1966.
Krogh, F.T.: A variable step variable order multistep method for the numerical solution of ordinary differential equations. Proceedings of the IFIP Congress 1968, Booklet A, pp. 91–95. Amsterdam: North-Holland Publ. Co., 1968.
Dahlquist, G.: Stability and error bounds in the numerical integration of ordinary differential equations. Trans. Roy. Inst. Technol., Stockholm. Nr. 130, 1959.
Spijker, M.N.: Stability and convergence of finite-difference methods (Thesis). Leiden University, 1968.
Henrici, P.: The propagation of round-off error in the numerical solution of initial value problems involving ordinary differential equations of the second order. Symposium, Provisional International Computation Centre, pp.275–289 (1960).
Timlake W.: On the numerical solution of special second order initial value problems (Thesis). Swiss Federal Institute of Technology, Zürich, 1963.
Timlake W.: An extension of the Σ2 procedure. Numer. Math. 7, 261–268 (1965).
Spijker, M.N.: Reduction of round-off error by splitting of difference formulae (submitted for publication).
Dyer, J.: Generalized multistep methods in satellite orbit computation. J. Assoc. Comput. Mach. 15, 712–719 (1968).
Collatz, L.: The numerical treatment of differential equations. Berlin: Springer-Verlag, 1960.
Spijker, M.N.: Convergence and stability of step-by-step methods for the numerical solution of initial-value problems. Numer. Math. 8, 161–177 (1966).
Metté, A.: Essai de résolution du problème de Goursat par la methode de Runge-Kutta pour une equation aux dérivées partielles du type hyperbolique. Rev. Française Informat. Recherche Opérationelle 1, 67–90 (1967).
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Spijker, M.N. (1969). Round-off error in the numerical solution of second order differential equations. In: Morris, J.L. (eds) Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics, vol 109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060036
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DOI: https://doi.org/10.1007/BFb0060036
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