Numerical Solution of Second Order Fuzzy Ordinary Differential Equations using Two-Step Block Method with Third and Fourth Derivatives

Authors

  • Kashif Hussain School of Quantitative Sciences, Universiti Utara Malaysia, Kedah, Malaysia
  • Oluwaseun Adeyeye School of Quantitative Sciences, Universiti Utara Malaysia, Kedah, Malaysia
  • Nazihah Ahmad School of Quantitative Sciences, Universiti Utara Malaysia, Kedah, Malaysia

Keywords:

Fuzzy initial value problem, Fuzzy boundary value problem, Second order, Two-step, Block method, Linear, Nonlinear

Abstract

Fuzzy differential equation models are suitable where uncertainty exists for real-world phenomena. Numerical techniques are used to provide an approximate solution to these models in the absence of an exact solution. However, existing studies that have developed numerical techniques for solving second-order fuzzy ordinary differential equations (FODEs) possess an absolute error accuracy that could be improved. Therefore, this article developed a more accurate higher derivative self-starting block scheme for the numerical solution of second-order FODEs with fuzzy initial and boundary conditions imposed. Linear block approach using Taylor series expansion is adopted for the derivation of the proposed method and the basic properties are established using the definitions of stability and consistency for block methods. According to the numerical results, when compared to the exact solution in terms of absolute error, the new method proposed in this article outperformed existing numerical methods. It is thus concluded that the proposed method is effective for solving second-order FODEs directly.

Dimensions

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Published

2023-04-04

How to Cite

Numerical Solution of Second Order Fuzzy Ordinary Differential Equations using Two-Step Block Method with Third and Fourth Derivatives. (2023). Journal of the Nigerian Society of Physical Sciences, 5(2), 1087. https://doi.org/10.46481/jnsps.2023.1087

Issue

Volume 5, Issue 2, May 2023

Section

Original Research
Copyright & Licensing

Copyright (c) 2023 Kashif Hussain, Oluwaseun Adeyeye, Nazihah Ahmad

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How to Cite

Numerical Solution of Second Order Fuzzy Ordinary Differential Equations using Two-Step Block Method with Third and Fourth Derivatives. (2023). Journal of the Nigerian Society of Physical Sciences, 5(2), 1087. https://doi.org/10.46481/jnsps.2023.1087