Well ordered monotone iterative technique for nonlinear second order four point Dirichlet BVPs

• Published in: Mathematical modelling and analysis Vol. 27; no. 1; pp. 59 - 77
• Main Authors: Verma, Amit, Urus, Nazia
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 07.02.2022
• Subjects: Boundary value problems; Continuity (mathematics); Dirichlet problem; Green's functions; green’s function; Iterative methods (Mathematics); Mathematical research; Maximum principle; monotone iterative technique; Sequences; Series, Dirichlet; India; maximum principle; Green’s function; monotone iterative technique
• ISSN: 1392-6292; 1648-3510; 1648-3510
• DOI: 10.3846/mma.2022.14198

In this article, we develop a monotone iterative technique (MI-technique) with lower and upper (L-U) solutions for a class of four-point Dirichlet nonlinear boundary value problems (NLBVPs), defined as,  where , the non linear term is continuous function in x, one sided Lipschitz in ψ and Lipschitz in . To show the existence result, we construct Green’s function and iterative sequences for the corresponding linear problem. We use quasilinearization to construct these iterative schemes. We prove maximum principle and establish monotonicity of sequences of lower solution  and upper solution such that   Then under certain sufficient conditions we prove that these sequences converge uniformly to the solution ψ(x) in a specific region where