A constructive monotone iterative method for second-order BVP in the presence of lower and upper solutions

• Published in: Applied mathematics and computation Vol. 123; no. 1; pp. 75 - 91
• Main Authors: Cherpion, M., De Coster, C., Habets, P.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 10.09.2001; Elsevier
• Subjects: Computable approximations; Exact sciences and technology; Lower and upper solutions; Mathematical analysis; Mathematics; Monotone iterative method; Neumann problem; Ordinary differential equations; Sciences and techniques of general use; Lower and upper solutions; Neumann problem; Computable approximations; Monotone iterative method; Second order equation; Inferior solution; Differential equation; Monotone approximation; Iterative method; Computable solution; Upper solution; Computability; Boundary value problem; Dirichlet problem; Approximate solution; Monotonicity
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/S0096-3003(00)00058-8

This paper concerns the monotone approximations of solutions of boundary value problems such as −u″+f(t,u,u ′)=0, 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 ( α⩽ β) or the other ( α⩾ β). We also consider the periodic and the Dirichlet problems.