An Analytic Solution for Riccati Matrix Delay Differential Equation using Coupled Homotopy-Adomian Approach

Main Article Content

Khalid Hammood AL-Jizani
https://orcid.org/0000-0002-8521-2090
Jawad Kadhim K. Al-Delfi
https://orcid.org/0000-0001-5612-9063

Abstract

An efficient modification and a novel technique combining the homotopy concept with  Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced  in this paper  . Both methods are very efficient and effective. The whole integral part of ADM is used instead of the integral part of homotopy technique. The major feature in current technique gives us a large convergence region of iterative approximate solutions .The results acquired by this technique give better approximations for a larger region as well as previously. Finally, the results conducted via suggesting an efficient and easy technique, and may be addressed to other non-linear problems.

Article Details

How to Cite
1.
An Analytic Solution for Riccati Matrix Delay Differential Equation using Coupled Homotopy-Adomian Approach. Baghdad Sci.J [Internet]. 2022 Aug. 1 [cited 2024 Nov. 22];19(4):0800. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/5752
Section
article

How to Cite

1.
An Analytic Solution for Riccati Matrix Delay Differential Equation using Coupled Homotopy-Adomian Approach. Baghdad Sci.J [Internet]. 2022 Aug. 1 [cited 2024 Nov. 22];19(4):0800. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/5752

References

Belal B, Mohamed S, Ishak H. Approximate solutions of singular two-point BVPs by modified homotopy analysis method. Phys. Lett. A. 2008; 372 (22): 4062-4066.

Sami Al, Mohd Salmi Md, Alomari A. Numerical Solution of Fractional-Order HIV Model Using Homotopy Method. DDNS. 2020; 2020: 1-13.

Alao S, Oderinu R, Akinpelu F, Akinola E. Homotopy Analysis Decomposition Method for the Solution of Viscous Boundary Layer Flow Due to a Moving Sheet. J. Adv. Math. Comp. Sci.. 2019; 32(5): 1-7.

AL-Jawary M, Rhahdi G, Ravnik J. Boundary-domain Integral Method and Homotopy Analysis Method for Systems of Nonlinear Boundary Value Problems in Environmental Engineering. Arab. J. Basic Appl. Sci. 2020; 27(1): 121-133.

Chi-Min L, Ray-Yeng Y. Application of Adomian Decomposition Method to Bounded and Unbounded Stokes’ Problems. Math. Probl. Eng. 2018; 2018: 1-11.

Mohammad A. Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Nonlinear and Volterra Integral Equations. Math. Stat. J. 2020; 8(3): 278-285.

Al-Mazmumy M, Almuhalbedi S. Modified Decomposition Method by Adomian and Rach for Solving Nonlinear Volterra Integro Differential Equations. Nonlinear Analy. Differ. Equ. 2017; 5(4): 157-170.

Rasool S, Hassan K, Muhammad A, Poom K. Application of Laplace-Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations. Entropy. 2019; 21(4): 1-17.

Béyi B, Justin L, Joseph B, Gabriel B. Application of the Adomian Decomposition Method (ADM) for Solving the Singular Fourth-Order Parabolic Partial Differential Equation. J. Appl. Math. Phys. 2018; 6(7): 1476-1480.

Abazari, R. Solution of Riccati types matrix differential equations using matrix differential transform method, J. Appl. Math. Informatics,2009; 27(5-6): 1133 -1143.

Khalid H, Noor A, Fadhel S. Variational Iteration Method for Solving Riccati Matrix Differential Equations. Indones. J. Electr Eng. Comput. Sci. 2017; 5(3): 673-683.

Shaher M, Asad F, Mohammed A. Analytical Study of Fractional-Order Multiple Chaotic FitzHugh- Nagumo Neurons Model Using Multistep Generalized Differential Transform Method. Abs. Appl. Analysis. 2014;2014(27): 1-10.

Mohammed A, Omar A, Shaher M. Numerical computations of coupled fractional resonant Schrödinger equations arising in quantum mechanics under conformable fractional derivative sense. Phys. Scripta. 2020; 95(7): 1-9.

Mohammed A, Asad F, Omar A, Nabil S. A Novel Multistep Generalized Di§erential Transform Method for Solving Fractional-order L¸ Chaotic and Hyperchaotic Systems. 2015; 19(4): 713-724.

Mohammed H, Ghaleb N. On the Homotopy Analysis Method for Fractional SEIR Epidemic Model.Res. J. Appl. Sci. Eng. Technol. 2014; 7(18): 3809-3820.

Similar Articles

You may also start an advanced similarity search for this article.