About the existence and uniqueness of solutions for some second-order nonlinear BVPs

Sonia Yadav, Sukhjit Singh, M.A. Hernández-Verón, Eulalia Martínez, Ajay Kumar and R.P. Badoni

Applied Mathematics and Computation, 2023, vol. 457, issue C

Abstract: The significance of our work is to solve some second-order nonlinear boundary value problems. To do this, we take into account the equivalence of the problems considered with certain integral equations, we will obtain a fixed-point-type result for these integral equations. This result provides us the existence and uniqueness of solutions for the second-order nonlinear boundary value problems considered. As a novelty, we will use for this fixed-point-type result a family of third order iterative processes to approximate the solution, instead of the usually considered method of Successive Approximations of linear convergence.

Keywords: Global Convergence; Convergence Balls; Third order Iterative Process; Recurrence Relations; Integral Equations (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:457:y:2023:i:c:s0096300323003879

DOI: 10.1016/j.amc.2023.128218

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