On numerical solution of ordinary differential equations with discontinuities
Jankowski, Tadeusz
Applications of Mathematics, Tome 33 (1988), p. 487-492 / Harvested from Czech Digital Mathematics Library
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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 $O(h^v)$.

Publié le : 1988-01-01
Classification:  34A34,  65L05 
@article{104326,
     author = {Tadeusz Jankowski},
     title = {On numerical solution of ordinary differential equations with discontinuities},
     journal = {Applications of Mathematics},
     volume = {33},
     year = {1988},
     pages = {487-492},
     zbl = {0671.65061},
     mrnumber = {0973242},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104326}
}

Jankowski, Tadeusz. On numerical solution of ordinary differential equations with discontinuities. Applications of Mathematics, Tome 33 (1988) pp. 487-492. http://gdmltest.u-ga.fr/item/104326/

I. Babuška M. Práger E. Vitásek Numerical processes in differential equations, SNTL, Praha 1966. (1966) | MR 0223101

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. (1974) | Article | MR 0381316

E. A. Coddington N. Levinson Theory of ordinary differential equations, Mc Graw-Hill, New York 1955. (1955) | MR 0069338

A. Feldstein R. Goodman Numerical solution of ordinary and retardea differential equations with discontinuous derivatives, Numer. Math. 21 (1973), 1-13. (1973) | Article | MR 0381320

P. Henrici Discrete variable methods in ordinary differential equations, J. Wiley, New York 1968. (1968) | MR 0135729

T. Jankowski Some remarks on numerical solution of initial problems for systems of differential equations, Apl. Mat. 24 (1979), 421 - 426. (1979) | MR 0547045 | Zbl 0447.65039

T. Jankowski On the convergence of multistep methods for ordinary differential equations with discontinuities, Demostratio Math. 16 (1983), 651 - 675. (1983) | MR 0733727 | Zbl 0571.65065

D. P. Squier One-step methods for ordinary differential equations, Numer. Math. 13 (1969), 176-179. (1969) | Article | MR 0247773 | Zbl 0182.21901

J. Szarski Differential inequalities, PWN- Polish. Scient. Publ., Warsaw 1967. (1967) | Zbl 0177.39203