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A constructive monotone iterative method for second-order BVP in the presence of lower and upper solutions. (English) Zbl 1024.65063
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.

65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
Full Text: DOI
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