Quasilinearization variational iteration method for system of nonlinear ODEs

In this manuscript, we discuss a new technique for solving system of nonlinear differential equations, which is a modification of the variation iteration method (VIM) implemented using the quasilinearization method and Adomian's polynomial. The quasilinearization variational iteration method (QVIM) is the name given to this proposed method. The proposed method's convergence analysis in Banach space is also discussed here. Three application problems, including the Genesio-Tesi system, are considered to test the applicability of our approach. We also discuss the case study of the chaotic and non-chaotic solutions of the Genesio-Tesi system (GTS). The convergence behaviour of the method is studied for various values of parameter x. To assess the viability and efficacy of QVIM, we compare it to the existing well-known Adomian decomposition method. The results show that the proposed method is highly efficient and simple to implement.