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discontinuities; system; one-step method; convergence; order of convergence; numerical solution of differential equations
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 $O(h^v)$.
[1] I. Babuška M. Práger E. Vitásek: Numerical processes in differential equations. SNTL, Praha 1966. MR 0223101
[2] B. A. Chartres R. S. Stepleman: Actual order of convergence of Runge-Kutta methods on differential equations with discontinuities. SIAM J. Numer. Anal. 11 (1974), 1193-1206. DOI 10.1137/0711090 | MR 0381316
[3] E. A. Coddington N. Levinson: Theory of ordinary differential equations. Mc Graw-Hill, New York 1955. MR 0069338
[4] A. Feldstein R. Goodman: Numerical solution of ordinary and retardea differential equations with discontinuous derivatives. Numer. Math. 21 (1973), 1-13. DOI 10.1007/BF01436181 | MR 0381320
[5] P. Henrici: Discrete variable methods in ordinary differential equations. J. Wiley, New York 1968. MR 0135729
[6] T. Jankowski: Some remarks on numerical solution of initial problems for systems of differential equations. Apl. Mat. 24 (1979), 421 - 426. MR 0547045 | Zbl 0447.65039
[7] T. Jankowski: On the convergence of multistep methods for ordinary differential equations with discontinuities. Demostratio Math. 16 (1983), 651 - 675. MR 0733727 | Zbl 0571.65065
[8] D. P. Squier: One-step methods for ordinary differential equations. Numer. Math. 13 (1969), 176-179. DOI 10.1007/BF02163235 | MR 0247773 | Zbl 0182.21901
[9] J. Szarski: Differential inequalities. PWN- Polish. Scient. Publ., Warsaw 1967. Zbl 0177.39203
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