Abstract
This paper is concerned with the numerical integration of ordinary differential equations of the orderx. Sufficient conditions and also necessary ones are given for the s-th difference quotient of the approximate solution to approach thes-th derivative of the exact solution fors >0. This requires a more subtle examination of the multiplicities of the characteristic roots of modulus 1.
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The work reported in this paper was started when the author was a member of the Institut für Praktische Mathematik (Prof. Dr. Dr. h. c.A. Walther), Technische Hochschule, Darmstadt, Germany.
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Dejon, B. Stronger than uniform convergence of multistep difference methods. Numer. Math. 8, 29–41 (1966). https://doi.org/10.1007/BF02165236
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DOI: https://doi.org/10.1007/BF02165236