**New Algorithm for Computing Adomian’s Polynomials to Solve Coupled Hirota System**

Rebwar S. Muhammad1*
, Rostam K. Saeed2 & Davron A. Juraev3

1Department of Mathematics, College of Education, University of Sulaimani, Sulaimani, Kurdistan Region, Iraq

2Department of Mathematics, College of Science, Salahaddin University/Erbil, Erbil-Iraq

3Chair of natural sciences disciplines, Higher Military Aviation School of the Republic of Uzbekistan, Jaykhun Street 180100, Karshi,
Uzbekistan

*Corresponding author Email:rebwar.muhammed@univsul.edu.iq

**Abstract**In this paper, when compared to the normal Adomian decomposition approach, we
updated the method of calculating Adomian's polynomial to discover the numerical
solution for a non-linear coupled Hirota system (CHS) with fewer components,
improved accuracy, and faster convergence (ADM). The novel algorithm offers a viable
way to computing Adomian polynomials for all types of non-linearity. We can see that
these two methods are both effective for solving non-linear CHS, however, the result
provided by our new algorithm is superior to that obtained by the classic Adomian
decomposition method. Maple 15 was utilized to do calculations in our work.

**Key Words:**Adomian Decomposition Method; Adomian’s Polynomial; Coupled Hirota System; Analytical Solution.

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