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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

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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