Abstract
This study introduces the Modified New Iterative Method (MNIM) for solving linear delay differential equations (LDDEs) and enhancing accuracy with a post-treatment iterative technique. Key concepts, including LDDEs and El-Kalla polynomials, are outlined. MNIM`s validity is confirmed through test cases, showing precise approximations with minimal error. The method proves efficient and reliable.
Key-Words / Index Term
Linear delay differential equations, El-Kalla polynomials, Adomian polynomials
References
[1] P. A. Ashitha and M. C. Ranjini, "On the numerical solution of fractional Riccati differential equations," Malaya Journal of Matematik, vol. 5, no. 1, pp. 214–219, 2020.
[2] V. Daftardar-Gejji and S. Bhalekar, "Solving fractional boundary value problems with Dirichlet boundary conditions using a new iterative method," Computers and Mathematics with Applications, vol. 59, no. 5, pp. 1801–1809, 2010.
[3] V. Daftardar-Gejji and H. Jafari, "An iterative method for solving nonlinear functional equations," Journal of Mathematical Analysis and Applications, vol. 316, pp. 753–763, 2006
[4] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method. Springer, 1994.
[5] R. Bellman and K. L. Cooke, Differential-Difference Equations. Academic Press, 1963.
[6] A. Bellen and M. Zennaro, Numerical Methods for Delay Differential Equations. Oxford University Press, 2003.
[7] M. J. Du, "A specific method for solving fractional delay differential equation via Fraction Taylor’s series," Mathematical Problems in Engineering, vol. 2022, pp. 1–6, 2022.
[8] I. L. El-Kalla, K. M. A. Elgaber, A. R. Elmahdy, and A. Y. Sayed, "Solution of a nonlinear delay differential equation using Adomian decomposition method with accelerated formula of Adomian polynomial," American Journal of Computational Mathematics, vol. 9, no. 4, pp. 221–233, 2019.
[9] P. Goswami and R. T. Alqahtani, "Solutions of fractional differential equations by Sumudu transform and variational iteration method," Journal of Nonlinear Science and Applications, vol. 9, no. 4, pp. 1944–1951, 2016.
[10] S. T. Mohyud-din and A. Yildirim, "Variational iteration method for delay differential equations using He’s polynomials," HITEC U, vol. 1, no. 2, pp. 1045–1048, 2010.
[11] A. T. Moltot and A. T. Deresse, "Approximate analytical solution to nonlinear delay differential equations by using Sumudu iterative method," Advances in Mathematical Physics, vol. 2022, no. 2, pp. 1–6, 2022.
Citation
Ibrahim M.D., Okai J.O., Michael Cornelius, "A Robust Numerical Method for Solving Linear Delay Differential Equations," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.6, pp.86-90, 2024