In this research, we find the optimal parameters for a nonlinear Belousov-Zhabofinkii system(BZS) using a method that is a mix of the genetic algorithm and (MADM) (modified Adomian decomposition method), which we will call GA MADM for short. When we use a fitness function that is tailored to the issue at hand, we discover that the optimal parameters result in considerably more desirable solutions. The findings demonstrated that the approximate solutions were sufficiently close to the precise answers, and the results also shown that the suggested method is more accurate and efficient than MADM, which makes use of parameters that were previously selected.
we will apply the modified Adomian decomposition approach in conjunction with the evolutionary algorithm to solve the nonlinear Belousov-Zhabofinkii system (GA). GA MADM's primary objective is to identify the optimal parameters for the nonlinear Belousov-Zhabofinkii system (c,L,r,M,b), but it may also be used to solve a broad variety of other nonlinear systems. In tables (2) and (3), our suggested approach GA-MADM ensures that the optimal parameters are identified precisely, even when the system is complex and has several values. Furthermore, it provides more accurate results than MADM. Through Figures (1), (2), and (3), our numerical results demonstrated that the approximate solutions generated by GA-MADM were quite close to the precise solutions (2). The computations for this paper were performed using the MAPLE 13 and Matlab® R2016a software packages.