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Zbl 1024.65063
Cherpion, M.; De Coster, C.; Habets, P.
A constructive monotone iterative method for second-order BVP in the presence of lower and upper solutions. (English)
[J] Appl. Math. Comput. 123, No.1, 75-91 (2001). ISSN 0096-3003

Summary: This paper concerns the monotone approximations of solutions of boundary value problems (BVPs) such as $$-u''+ f(t,u,u')= 0,\quad u'(0)= u'(1)= 0.$$ We consider linear iterative scheme in case $f$ is Lipschitz in $u'$ and satisfies a one-sided Lipschitz condition in $u$. The initial approximations are lower and upper solutions which can be ordered one way $(\alpha\le\beta)$ or the other $(\alpha\ge\beta)$. We also consider the periodic and the Dirichlet problems.

MSC 2000:: *65L10 Boundary value problems for ODE (numerical methods)
34B15 Nonlinear boundary value problems of ODE

Keywords: periodic problem; monotone iterative method; Neumann problem; lower and upper solutions; Dirichlet problems

Cited in: Zbl 1078.34007

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