Existence results for a class of four point nonlinear singular BVP arising in thermal explosion in a spherical vessel

Nazia Urus and Amit Kumar Verma

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 220, issue C, 516-532

Abstract: In this article, the following class of four-point singular non-linear boundary value problem (NLBVP) is considered which arises in thermal explosion in a spherical vessel −(s2y′(s))′=s2f(s,y,s2y′),s∈(0,1),y′(0)=0,y(1)=δ1y(η1)+δ2y(η2), where Ω=(0,1)×R2, f:Ω→R is continuous on Ω as well as satisfy Lipschitz condition with respect to y and y′ (one sided), δ1, δ2>0 are constants, and 0<η1≤η2<1. We provide an estimation of the region of existence of a solution of above singular NLBVP. We extend the theory of monotone iterative technique (MIT) which provides computable monotone sequences that converge to the solutions of the nonlinear four point BVPs.

Keywords: Monotone iterative technique; Upper and lower solutions; Green’s function (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:220:y:2024:i:c:p:516-532

DOI: 10.1016/j.matcom.2024.02.006

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