Further generalization of quasilinearization method with initial time difference. (English) Zbl 1200.34011

The method of the quasilinearization is applied to obtain upper and lower sequences with initial time difference in terms of linear differential equations that start at different initial times. It is also shown that these sequences converge to the unique solution of the following nonlinear equation uniformly and quadratically
\[ u'=N(t,u)=f(t,u)+g(t,u)+h(t,u),\;u(t_0)=u_0 \]
for \(t\geq t_0\), \(t_0\in \mathbb{R}^+\), where \(f,g,h\in C[\mathbb{R}^+\times\mathbb{R}, \mathbb{R}]\).
Reviewer: Minghe Pei (Jilin)


34A45 Theoretical approximation of solutions to ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations