Geodesic
On numerical solution of ordinary differential equations with discontinuities
Applications of Mathematics, Tome 33 (1988) no. 6, pp. 487-492.

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The author defines the numerical solution of a first order ordinary differential equation on a bounded interval in the way covering the general form of the so called one-step methods, proves convergence of the method (without the assumption of continuity of the righthad side) and gives a sufficient condition for the order of convergence to be $O(h^v)$.
DOI : 10.21136/AM.1988.104326
Classification : 34A34, 65L05
Keywords: discontinuities; system; one-step method; convergence; order of convergence; numerical solution of differential equations 
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     title = {On numerical solution of ordinary differential equations with discontinuities},
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Jankowski, Tadeusz. On numerical solution of ordinary differential equations with discontinuities. Applications of Mathematics, Tome 33 (1988) no. 6, pp. 487-492. doi : 10.21136/AM.1988.104326. http://geodesic.mathdoc.fr/articles/10.21136/AM.1988.104326/

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