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چکیده
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This study introduces a family of root-solvers for systems of nonlinear equations, leveraging the Daftardar–Gejji and Jafari Decomposition Technique coupled with the midpoint quadrature rule. Despite the existing application of these root solvers to single-variable equations, their extension to systems of nonlinear equations marks a pioneering advancement. Through meticulous deriva- tion, this work not only expands the utility of these root solvers but also presents a comprehensive analysis of their stability and semilocal convergence; two areas of study missing in the existing literature. The convergence of the proposed solvers is rigorously established using Taylor series expansions and the Banach Fixed Point Theorem, providing a solid theoretical foundation for semilocal convergence guarantees. Additionally, a detailed stability analysis further underscores the robustness of these solvers in various computational scenarios. The practical efficacy and ap- plicability of the developed methods are demonstrated through the resolution of five real-world application problems, underscoring their potential in addressing complex nonlinear systems. This research fills a significant gap in the literature by offering a thorough investigation into the sta- bility and convergence of these root solvers when applied to nonlinear systems, setting the stage for further explorations and applications in the field
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