Approximate Polynomial Solution for Two-Point Fuzzy Boundary Value Problems


Abstract views: 38 / PDF downloads: 50

Authors

  • Mazin H. Suhhiem Department of Mathematics, University of Sumer, Alrifaee
  • Raad I. Khwayyit Ministry of Education, Alrifaee

Abstract

In this research, we have used double decomposition method to find approximate analytical solutions for the two-point fuzzy boundary value problems. This method is based on the standard Adomian decomposition method, which is an approximation method that is used to solve fuzzy and non-fuzzy differential equations. This method allows for the solution to be calculated as a convergent series, This means that the solution is in the form of a polynomial that approaches the exact solution of the differential equation. The numerical solutions that we presented during this research showed the high efficiency of this method.

References

T. Allahviranloo and L. Jamshidi, Solution of Fuzzy Differential Equations Under Generalized Differentiability by Adomian Decomposition Method, Iranian Journal of Optimization, Vol. 1 (2009), 56-75.

L. Wang and S. Guo, Adomian Method for Second Order Fuzzy Differential Equations, World Academy of Science, Engineering and Technology, Vol. 52 (2011), 979-982.

J. Duan, R. Rach and D. Baleanu, A Review of the Adomian Decomposition method and Its Applications to Fractional Differential Equations, Commun. Frac. Calc., Vol. 3, No. 2 (2012), 73-99.

S. Narayanamoorthy and T. Yookesh, An Adomian Decomposition Method to Solve Linear Fuzzy Differential Equations, Proceeding of the International Conference on Mathematical Methods and Computation, India, 13-14 February 2014.

M. Paripour, E. Hajilou and A. Hajilou, Application of Adomian Decomposition Method to Solve Hybrid Fuzzy Differential Equations, Journal of Taibah University for Science, Vol. 9 (2015), 95-103.

A. Jameel, Numerical and Approximate – Analytical Solutions of Fuzzy Initial Value Problems, Ph.D. Thesis, School of Quantitative Sciences, University Utara Malaysia, Malaysia, 2015.

S. Biswas, S. Banerjee and T. Roy, Solving Intuitionistic Fuzzy Differential Equations with Linear Differential Operator by Adomian Decomposition Method, 3rd Int. IFS Conf., Turkey, Notes on Intuitionistic Fuzzy Sets, Vol. 22. No. 4 (2016), 25-41.

S. Biswas and T. Roy, Adomian Decomposition Method for Fuzzy Differential Equations with Linear Differential Operator, Journal of Information and Computing Science, Vol. 11, No. 4 (2016), 243-250.

M. Suhhiem, Fuzzy Artificial Neural Network For Solving Fuzzy and Non-Fuzzy Differential Equations, Ph.D. Thesis, College of Sciences, University of Al-Mustansiriyah, Iraq, 2016.

A. Ateeah, Approximate Solution for Fuzzy Differential Algebraic Equations of Fractional Order Using Adomian Decomposition Method, Ibn Al-Haitham J. for Pure & Appl. Sci., Vol. 30, No. 2 (2017) 202-213.

S. Askari, T. Allahviranloo and S. Abbasbandy, Solving Fuzzy Fractional Differential Equations by Adomian Decomposition Method Used in Optimal Control Theory, International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies,Vol. 10, No. 12 (2019), 1-10.

H. Sabr, B. Abood and M. Suhhiem, Fuzzy Homotopy Anaysis Method for Solving Fuzzy Autonomous Differential Equation, Ratio Mathematica, Vol. 40 (2021), 191-212.

N. AL-Zaid, A. AL-Refaidi and H. Bakodah, Solution of Second- and Higher-Order Nonlinear Two-Point Boundary-Value Problems Using Double Decomposition Method, Journal of Mathematics,10 , 3519 (2022), 1-15.

M. Suhhiem and R. Khwayyit, Semi Analytical Solution for Fuzzy Autonomous Differential Equations, International Journal of Analysis and Applications, Vol. 20 (2022), 1-18.

Downloads

Published

2023-12-20

How to Cite

Mazin H. Suhhiem, & Raad I. Khwayyit. (2023). Approximate Polynomial Solution for Two-Point Fuzzy Boundary Value Problems. Results in Nonlinear Analysis, 7(1), 64–79. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/248