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Jankowski, Tadeusz
Some remarks on numerical solution of initial problems for systems of differential equations. (English). Aplikace matematiky, vol. 24 (1979), issue 6, pp. 421-426
MSC: 65L05 | MR 0547045 | Zbl 0447.65039 | DOI: 10.21136/AM.1979.103825
Keywords:
systems; sufficient conditions for convergence; Gronwall inequality; error bound
Summary:
This paper presents a class of numerical methods for approximate solution of systems of ordinary differential equations. It is shown that under certain general conditions these methods are convergent for sufficiently small step size. We give estimations of errors which are better than the known ones.
References:
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[2] Hartman P.: Ordinary differential equations. New York: John Wiley and Sons 1964. MR 0171038 | Zbl 0125.32102
[3] Hayoshi K.: On stability of numerical solutions of a differential system by one-step methods. TRU Mathematics 5, 67-83 (1969). MR 0269123
[4] Henrici P.: Discrete variable methods in ordinary differential equations. New York: John Wiley and Sons 1968. MR 0135729
[5] Ohashi T.: On the conditions for convergence of one-step methods for ordinary differential equations. TRU Mathematics 6, 59-62 (1970). MR 0331791 | Zbl 0252.65054
[6] Squier D. P.: One-step methods for ordinary differential equations. Numer. Math. 13, 176-179 (1969). DOI 10.1007/BF02163235 | MR 0247773 | Zbl 0182.21901
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