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International Journal of Neutrosophic Science

Volume 25 , Issue 2 , PP: 165-175, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Numerical Proceduers for Computing the Exact Solutions to Systems of Ordinary Differential Equations

Nidal Anakira 1 * , Osama Oqilat 2 , Adel Almalki 3 , Irianto Irianto 4 , Saad Meqdad 5 , Ala Amourah 6

  • 1 Faculty of Education and Arts, Mathematics Section, Sohar University,Sohar 3111, Sultanat of Oman; Jadara University Research Center, Jadara University, Jordan - (nanakira@su.edu.om)
  • 2 Department of Basic Sciences, Faculty of Arts and Science, Al-Ahliyya Amman University, Amman 19328, Jordan - (o.oqilat@ammanu.edu.jo)
  • 3 Department of Mathematics, Al-Qunfudhah University College, Umm Al-Qura University, Mecca, Saudi Arbia - (aaamalki@uqu.edu.sa)
  • 4 Department General Education, Faculty of Resilience, Rabdan Academy, Abu Dhabi 22401, United Arab Emirates - (iharny@ra.ac.ae)
  • 5 Applied Science Private University, Amman, Jordan - (s_meq75@yahoo.com)
  • 6 Faculty of Education and Arts, Mathematics Section, Sohar University,Sohar 3111, Sultanat of Oman - (AAmourah@su.edu.om)

    • Doi: https://doi.org/10.54216/IJNS.250214

    Received: February 12, 2024 Revised: April 30, 2024 Accepted: August 04, 2024
    Abstract

    This paper presents a modified homotopy perturbation method (HPM), which aimed at solving systems of ordinary differential equations (ODEs). The MHPM, which combines the HPM, Laplace transform, and Padé approximants, offers an alternative approach to address the challenges associated with solving such problems. By employing this method, it becomes feasible to overcome these challenges and obtain a dependable approximation for the exact solution. The effectiveness and applicability of the proposed scheme are demonstrated through preliminary results derived from illustrative examples, all of which correspond to exact solutions.

    Keywords :

    Numerical Approximation , HPM , MHPM , Laplace transformation , Padé , approximants

    References

    [1]       Altaie, Sarmad A., Nidal Anakira, Ali Jameel, Osama Ababneh, Ahmad Qazza, and Abdel Kareem Alomari. "Homotopy analysis method analytical scheme for developing a solution to partial differential equations in fuzzy environment." Fractal and Fractional 6, no. 8 (2022): 419.

    [2]       Marinca V, Herişanu N. Application of optimal homotopy asymptotic method for solving nonlinear equations arising in heat transfer. International communications in heat and mass transfer. 2008 Jul 1;35(6):710-5.

    [3]       Jameela A, Anakira NR, Alomari AK, Hashim I, Shakhatreh MA. Numerical solution of n’th order fuzzy initial value problems by six stages. Journal of Nonlinear Science Applications. 2016;9(2):627-40. Biazar J, Ghazvini H, Eslami M. He’s homotopy perturbation method for systems of integro-differential equations. Chaos, Solitons & Fractals. 2009 Feb 15;39(3):1253-8.

    [4]       Alahmad, S., Anakira, N. R., Mamat, M., Sulaiman, I., & AlAhmad, R. (2022). Modified differential transformation method for solving classes of non-linear differential equations. TWMS Journal of Applied and Engineering Mathematics, 12(1), 107.

    [5]       Hemeda AA. Homotopy perturbation method for solving systems of nonlinear coupled equations. Applied Mathematical Sciences. 2012;6(96):4787-800.

    [6]       Amourah AA, Yousef F. Some properties of a class of analytic functions involving a new generalized differential operator. Boletim da Sociedade Paranaense de Matematica. 2020;38(6):33-42.

    [7]       Jameel AF, Shather AH, Anakira NR, Alomari AK, Saaban A. Comparison for the approximate solution of the second-order fuzzy nonlinear differential equation with fuzzy initial conditions. Math Stat 8: 527–534.

    [8]       Ramos JI. On the variational iteration method and other iterative techniques for nonlinear differential equations. Applied Mathematics and Computation. 2008 May 15;199(1):39-69.

    [9]       Anakira NR, Alomari AK, Hashim I. Application of optimal homotopy asymptotic method for solving linear delay differential equations. InAIP Conference Proceedings 2013 Nov 27 (Vol. 1571, No. 1, pp. 1013-1019). American Institute of Physics.

    [10]    Shang X, Han D. Application of the variational iteration method for solving nth-order integro-differential equations. Journal of Computational and Applied Mathematics. 2010 Jul 1;234(5):1442-7.

    [11]    Anakira N, Jameel A, Hijazi M, Alomari AK, Man N. A new approach for solving multi-pantograph type delay differential equations. International Journal of Electrical & Computer Engineering (2088-8708). 2022 Apr 1;12(2).

    [12]    Abualhomos, M. "Numerical ways for solving fuzzy differential equations." Int. J. Appl. Engin. Res 13 (2018): 4610-4613.Al-Ahmad S, Anakira NR, Mamat M, Suliman IM, AlAhmad R. Modified differential transformation scheme for solving classes of non-linear differential equations. TWMS J. Appl. Eng. Math. 2021.

    [13]    Ayaz F. Solutions of the system of differential equations by differential transform method. Applied Mathematics and Computation. 2004 Jan 12;147(2):547-67.

    [14]    Stević S. On a system of difference equations. Applied Mathematics and Computation. 2011 Dec 1;218(7):3372-8.

    [15]    Jameel, Ali Fareed, Nidal Ratib Anakira, A. K. Alomari, D. M. Alsharo, and Azizan Saaban. "New semi-analytical method for solving two point nth order fuzzy boundary value problem." International Journal of Mathematical Modelling and Numerical Optimisation 9, no. 1 (2019): 12-31.

    [16]    Burqan, Aliaa, Mona Khandaqji, Zeyad Al-Zhour, Ahmad El-Ajou, and Tasneem Alrahamneh. "Analytical Approximate Solutions of Caputo Fractional KdV‐Burgers Equations Using Laplace Residual Power Series Technique." Journal of Applied Mathematics 2024, no. 1 (2024): 7835548.

    [17]    Amourah AA, Yousef F, Al-Hawary T, Darus M. A certain fractional derivative operator for p-valent functions and new class of analytic functions with negative coefficients. Far East Journal of Mathematical Sciences. 2016 Jan 1;99(1):75.

    [18]    Subramanian M, Manigandan M, Tunç C, Gopal TN, Alzabut J. On system of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order. Journal of Taibah University for Science. 2022 Dec 31;16(1):1-23.

    [19]    Awawdeh, Fadi, M. Khandaqji, Z. Mustafa, and Mohammad Younis. "A new approach for the solution of the electrostatic potential differential equations." Mathematical Problems in Engineering 2009 (2009): 23.

    [20]    Jameel, Ali, N. R. Anakira, A. K. Alomari, and Noraziah H. Man. "Solution and analysis of the fuzzy Volterra integral equations via homotopy analysis method." Computer Modeling in Engineering & Sciences 127, no. 3 (2021): 875-899.

    [21]    Shams M, Kausar N, Alayyash K, Al-Shamiri MM, Arif N, Ismail R. Semi-analytical scheme for solving intuitionistic fuzzy system of differential equations. IEEE Access. 2023 Feb 1;11:33205-23.

    [22]    He JH. Homotopy perturbation method: a new nonlinear analytical technique. Applied Mathematics and computation. 2003 Feb 15;135(1):73-9.

    [23]    He JH. Homotopy perturbation technique. Computer methods in applied mechanics and engineering. 1999 Aug 1;178(3-4):257-62.

    [24]    Shakeri, F., & Dehghan, M. (2008). Solution of delay differential equations via a homotopy perturbation method. Mathematical and computer Modelling, 48(3-4), 486-498.

    [25]    Al-Ahmad S, Sulaiman IM, Mamat M, Ghazali PL. Modified differential transform scheme for solving systems of first order ordinary differential equations. J. Math. Comput. Sci. 2021;22:73-84.

    [26]    Al-Ahmad, S., I. M. Sulaiman, M. Mamat, and L. G. Puspa. "A Modification of Differential Transform Method for Solving Systems of Second Order Ordinary Differential Equations." (2020).

    [27]    Jameel, A. F., Anakira, N. R., Rashidi, M. M., Alomari, A. K., Saaban, A., & Shakhatreh, M. A. (2018). Differential Transformation Method For Solving High Order Fuzzy Initial Value Problems. Italian Journal of Pure and Applied Mathematics, 39, 194-208.

    [28]    Jameel, A. F., Anakira, N. R., Shather, A. H., Saaban, A., & Alomari, A. K. (2020). Numerical algorithm for solving second order nonlinear fuzzy initial value problems. International Journal of Electrical and Computer Engineering (IJECE), 10(6), 6497-6506.

    [29]    Anakira, N. R. (2018). Optimal homotopy asymptotic method for solving multi-pantograph type delay differential equations. Adv. Differ. Equ. Control Proc. 19 (3), 191-204.

    [30]    Anakira, N. R., Alomari, A. K., Jameel, A. F., & Hashim, I. (2017). Multistage optimal homotopy asymptotic method for solving boundary value problems with robin boundary conditions. Far East Journal of Mathematical Sciences, 102(8), 1727-1744.

    Cite This Article As :
    Anakira, Nidal. , Oqilat, Osama. , Almalki, Adel. , Irianto, Irianto. , Meqdad, Saad. , Amourah, Ala. Numerical Proceduers for Computing the Exact Solutions to Systems of Ordinary Differential Equations. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 165-175. DOI: https://doi.org/10.54216/IJNS.250214
    Anakira, N. Oqilat, O. Almalki, A. Irianto, I. Meqdad, S. Amourah, A. (2025). Numerical Proceduers for Computing the Exact Solutions to Systems of Ordinary Differential Equations. International Journal of Neutrosophic Science, (), 165-175. DOI: https://doi.org/10.54216/IJNS.250214
    Anakira, Nidal. Oqilat, Osama. Almalki, Adel. Irianto, Irianto. Meqdad, Saad. Amourah, Ala. Numerical Proceduers for Computing the Exact Solutions to Systems of Ordinary Differential Equations. International Journal of Neutrosophic Science , no. (2025): 165-175. DOI: https://doi.org/10.54216/IJNS.250214
    Anakira, N. , Oqilat, O. , Almalki, A. , Irianto, I. , Meqdad, S. , Amourah, A. (2025) . Numerical Proceduers for Computing the Exact Solutions to Systems of Ordinary Differential Equations. International Journal of Neutrosophic Science , () , 165-175 . DOI: https://doi.org/10.54216/IJNS.250214
    Anakira N. , Oqilat O. , Almalki A. , Irianto I. , Meqdad S. , Amourah A. [2025]. Numerical Proceduers for Computing the Exact Solutions to Systems of Ordinary Differential Equations. International Journal of Neutrosophic Science. (): 165-175. DOI: https://doi.org/10.54216/IJNS.250214
    Anakira, N. Oqilat, O. Almalki, A. Irianto, I. Meqdad, S. Amourah, A. "Numerical Proceduers for Computing the Exact Solutions to Systems of Ordinary Differential Equations," International Journal of Neutrosophic Science, vol. , no. , pp. 165-175, 2025. DOI: https://doi.org/10.54216/IJNS.250214

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