Mathematics (May 2025)

Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction

  • Kanyuta Poochinapan,
  • Sompop Moonchai,
  • Tanadon Chaobankoh,
  • Phakdi Charoensawan

DOI
https://doi.org/10.3390/math13101569
Journal volume & issue
Vol. 13, no. 10
p. 1569

Abstract

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A new kind of graph-based contraction in a metric space is introduced in this article. We investigate results concerning the best proximity points and fixed points for these contractions, supported by illustrated examples. The practical applicability of our results is demonstrated through particular instances in the setting of integral equations and differential equations. We also describe how a class of third-order boundary value problems satisfying the present contraction can be solved iteratively. To support our findings, we conduct a series of numerical experiments with various third-order boundary value problems.

Keywords