Kounadis, A. N. An efficient and simple approximate technique for solving nonlinear initial and boundary-value problems. (English) Zbl 0757.65083 Comput. Mech. 9, No. 3, 221-231 (1992). A Picard-Lindelöf type iteration is proposed for solving nonlinear initial or boundary-value problems. Convergence of the iteration is proved. Its efficiency is demonstrated by two examples. Reviewer: E.Hairer (Genève) Cited in 4 Documents MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:Picard-Lindelöf iteration; upper bound error estimates; successive approximations; nonlinear initial or boundary-value problems; Convergence PDF BibTeX XML Cite \textit{A. N. Kounadis}, Comput. Mech. 9, No. 3, 221--231 (1992; Zbl 0757.65083) OpenURL