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On numerical solution of ordinary differential equations with discontinuities. (English) Zbl 0671.65061
The author considers the initial value problem for the system of ordinary differential equations (1) \(y'=f(t,y)\), \(y(a)=y_ 0\) on \(I=<a,b>\) where the function f is of Caratheodory’s type and satisfies the Perron condition. A bounded function x is a solution of (1) if it is absolutely continuous on I, satisfies the initial condition and the equation almost everywhere on I. Let h be, as usually, the step size and let v(i,h) be an arbitrary sequence (may be generated by a one-step method). Sufficient conditions for convergence of v to the solution x and sufficient conditions for the order of convergence to be \(O(h^ p)\) are formulated.
Reviewer: Z.Schneider
MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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References:
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