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

Author

Listed:
  • Kanyuta Poochinapan

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand)

  • Sompop Moonchai

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand)

  • Tanadon Chaobankoh

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand)

  • Phakdi Charoensawan

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand)

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.

Suggested Citation

  • Kanyuta Poochinapan & Sompop Moonchai & Tanadon Chaobankoh & Phakdi Charoensawan, 2025. "Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction," Mathematics, MDPI, vol. 13(10), pages 1-24, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1569-:d:1652786
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    References listed on IDEAS

    as
    1. Abushammala, Mariam & Khuri, S.A. & Sayfy, A., 2015. "A novel fixed point iteration method for the solution of third order boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 131-141.
    2. Simeon Reich & Alexander J. Zaslavski, 2021. "Contractive Mappings on Metric Spaces with Graphs," Mathematics, MDPI, vol. 9(21), pages 1-8, November.
    3. Syeda Tehmina Ejaz & Ghulam Mustafa, 2016. "A Subdivision Based Iterative Collocation Algorithm for Nonlinear Third‐Order Boundary Value Problems," Advances in Mathematical Physics, John Wiley & Sons, vol. 2016(1).
    4. Jamilu Abubakar Jiddah & Monairah Alansari & Om Kalthum S. K. Mohammed & Mohammed Shehu Shagari & Awad A. Bakery & Sumit Chandok, 2023. "Fixed Point Results of a New Family of Contractions in Metric Space Endowed with a Graph," Journal of Mathematics, Hindawi, vol. 2023, pages 1-9, April.
    5. Syeda Tehmina Ejaz & Ghulam Mustafa, 2016. "A Subdivision Based Iterative Collocation Algorithm for Nonlinear Third-Order Boundary Value Problems," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-14, June.
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