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Mathematics
Volume 13
Issue 10
10.3390/math13101569
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

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

by
Kanyuta Poochinapan
1,2,3,
Sompop Moonchai
1,2,3,*,
Tanadon Chaobankoh
1,2,3 and
Phakdi Charoensawan
1,2,3,*
1
Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
2
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
3
Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand
*
Authors to whom correspondence should be addressed.
Mathematics 2025, 13(10), 1569; https://doi.org/10.3390/math13101569 (registering DOI)
Submission received: 25 March 2025 / Revised: 30 April 2025 / Accepted: 2 May 2025 / Published: 9 May 2025
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications: 3rd Edition)
Versions Notes

Abstract

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: contraction; differential equation; integral equation contraction; differential equation; integral equation

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MDPI and ACS Style

Poochinapan, K.; Moonchai, S.; Chaobankoh, T.; Charoensawan, P. Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction. Mathematics 2025, 13, 1569. https://doi.org/10.3390/math13101569

AMA Style

Poochinapan K, Moonchai S, Chaobankoh T, Charoensawan P. Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction. Mathematics. 2025; 13(10):1569. https://doi.org/10.3390/math13101569

Chicago/Turabian Style

Poochinapan, Kanyuta, Sompop Moonchai, Tanadon Chaobankoh, and Phakdi Charoensawan. 2025. "Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction" Mathematics 13, no. 10: 1569. https://doi.org/10.3390/math13101569

APA Style

Poochinapan, K., Moonchai, S., Chaobankoh, T., & Charoensawan, P. (2025). Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction. Mathematics, 13(10), 1569. https://doi.org/10.3390/math13101569

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