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

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  • Urus, Nazia
  • Verma, Amit Kumar

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.

Suggested Citation

  • Urus, Nazia & Verma, Amit Kumar, 2024. "Existence results for a class of four point nonlinear singular BVP arising in thermal explosion in a spherical vessel," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 516-532.
    • Handle: RePEc:eee:matcom:v:220:y:2024:i:c:p:516-532
    DOI: 10.1016/j.matcom.2024.02.006
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    1. Alberto Cabada & Lucía López-Somoza & Mouhcine Yousfi, 2021. "Green’s Function Related to a n -th Order Linear Differential Equation Coupled to Arbitrary Linear Non-Local Boundary Conditions," Mathematics, MDPI, vol. 9(16), pages 1-14, August.
    2. Mei Wei & Qiang Li, 2017. "Monotone Iterative Technique for a Class of Slanted Cantilever Beam Equations," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-8, December.
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