An efficient and simple approximate technique for solving nonlinear initial and boundary-value problems. (English) Zbl 0757.65083

Kounadis, A. N.

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)

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