Numerical solution of random ordinary differential equations by using modified decomposition method
*Khansaa Majeed JaradCorresponding authorkhansaamajead@gmail.comkhansaamajeed@uomustansiriyah.edu.iqDepartment of MathematicsCollege of EducationMustansiriyah UniversityBaghdad, IraqView full profile → , Ali Adnan Abdulsahibalialkdhimi@uomustansiriyah.edu.iqDepartment of MathematicsCollege of EducationMustansiriyah UniversityBaghdad, IraqView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 11 Mar 2025
- Published Online:
- 14 Jan 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2245
- Pages:
- 105–112
Abstract
Keywords
Subject Classifications
References
[1] T. T. Soong, Random Differential Equations in Science and Engineering, vol. 103. New York: Academic Press (1973).
[2] L. Arnold, Stochastic Differential Equations: Theory and Applications. New York: John Wiley & Sons (1974).
[3] R. Jain, K. Arekar, and R. S. Dubey, “Study of Bergman’s minimal blood glucose-insulin model by Adomian decomposition method,” J. Inf. Optim. Sci., vol. 38, no. 1, pp. 133–149 (2017), doi: 10.1080/02522667.2016.1187919.
[4] K. Nouri and H. Ranjbar, “Mean square convergence of the numerical solution of random differential equations,” Mediterranean Journal of Mathematics, vol. 12, pp. 1123–1140 (2015), doi:10.1007/s00009-014-0452-8.
[5] X. Han and P. E. Kloeden, Random Ordinary Differential Equations and Their Numerical Solution. Singapore: Springer Nature (2017).
[6] S. F. Fadhel, A. A. Abdulsahib, and S. H. Abid, “Solution of random ordinary differential equations using Laplace variational iteration method,” Ital. J. Pure Appl. Math., no. 46, pp. 71–81 (2021).
[7] A. A. Abdulsahib and S. F. Fadhel, “Solution of fractional order random integro-differential equations using homotopy perturbation method,” AIP Conf. Proc., vol. 2457, Art. no. 020001 (2023).
[8] A. A. Abdulsahib, S. F. Fadhel, and J. H. Eidi, “Approximate solution of linear fuzzy random ordinary differential equations using Laplace variational iteration method,” Iraqi J. Sci., vol. 65, no. 2, pp. 804–817 (2024), doi: 10.24996/ijs.2024.65.2.18.
[9] I. S. Ahmed, A. Al-fayadh, H. H. Ebrahim, and L. S. Abdalbaqi, “Implementation of the Neutrosophic Sets in Measurable Space with Respect to Neutrosophic Ring,” Int. J. Neutrosophic Sci., vol. 25, no. 3, pp. 187–193 (2025), https://doi.org/10.54216/IJNS.250317
[10] G. Adomian and R. Rach, “Modified decomposition solution of linear and nonlinear boundary-value problems,” Nonlinear Anal., vol. 23, pp. 615–619 (1994).
[11] A. M. Wazwaz, “Approximate solutions to boundary value problems of higher order by the modified decomposition method,” Comput. Math. Appl., vol. 40, pp. 679–691 (2000).
[12] A. Abdulrazak and D. Pelinovsky, “Convergence of the Adomian decomposition method for initial-value problems,” Wiley Online Library (2009), doi: 10.1002/num.20549.
[13] X. Zhang, F. A. Shah, Y. Li, L. Yan, A. Q. Baig, and M. R. Farahani, “A family of fifth-order convergent methods for solving nonlinear equations using variational iteration technique,” J. Inf. Optim. Sci., vol. 39, no. 3, pp. 673–694 (2018), doi: 10.1080/02522667.2018.1443628.
[14] J. H. Eidi, E. M. Hameed, and J. R. Kider, “Convex fuzzy distance between two convex fuzzy compact sets,” J. Interdiscip. Math., vol. 27, no. 4, pp. 953–963 (2024), doi: 10.47974/JIM-1916.
[15] V. Krishnan, Nonlinear Filtering and Smoothing. New York: John Wiley & Sons (1984).
[16] P. E. Kloeden and E. Platen, The Numerical Solution of Stochastic Differential Equations, 2nd ed., vol. 23, Applications of Mathematics. Berlin: Springer-Verlag (1995).
