Open AccessWELL ORDERED MONOTONE ITERATIVE TECHNIQUE FOR NONLINEAR SECOND ORDER FOUR POINT DIRICHLET BVPS
Author(s) -
Amrisha Verma,
Nazia Urus
Publication year - 2022
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/mma.2022.14198
Subject(s) - mathematics , lipschitz continuity , monotone polygon , monotonic function , nonlinear system , iterative method , dirichlet distribution , function (biology) , mathematical analysis , boundary value problem , mathematical optimization , geometry , physics , quantum mechanics , evolutionary biology , biology
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