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On approximate Picard’s iterates for multipoint boundary value problems. (English) Zbl 0567.65054
Der Gegenstand der Arbeit ist die Differentialgleichung n-ter Ordnung \(x^{(n)}=f(t,x(t),x'(t),...,x^{(q)}(t)),\) \(0\leq q\leq n-1\) mit den Mehrpunktrandwertbedingungen \(x^{(j)}(a_ i)=A_{j+1,i}\); \(0\leq j\leq k_ i\), \(1\leq i\leq r\), \(a_ 1<a_ 2<...<a_ r\), \(0\leq k_ i\), \(\sum^{r}_{i=1}k_ i+r=n,\quad r\geq 2.\) Es werden Fragen der Existenz und der Eindeutigkeit im Zusammenhang mit der Lipschitz- Stetigkeit der Funktion f diskutiert. Außerdem wird die Picardsche Methode der sukzessiven Approximation untersucht, wobei man den Fall betrachtet, daß die Funktion f durch eine approximierende Funktion \(f^*\) ersetzt wird. Fehlerabschätzungen werden angegeben, und ein konkretes Beispiel illustriert die gegebene Theorie.
Reviewer: A.Huťa jun

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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