Monotone iteration descretization algorithm for BVP's
This paper deals with the following weakly nonlinear boundary value problem \(-u''+g(x,u(x))=0,\) \(u(a)=u(b)=0.\) By means of available estimations lower and upper solutions are generated. Authors replace the optimization by implementable estimations and propose a monotone iteration technique for the finite-dimensional problem in such a way that enclosures are obtained in each iteration step of the method. Finally, numerical realizations are given using interval arithmetic.
scientific article; zbMATH DE number 4082882