The modified decomposition method for solving nonlinear algebraic equations
This paper proposes an exact method for solving nonlinear algebraic equations in one unknown. The method consists of expressing the solution of the nonlinear equation as an infinite series, the terms of which are generalized polynomials. The author develops the technique proposed before by \textit{K. Abbaoui} and \textit{Y. Cherruault} [Math. Comput. Modelling 20, 69-73 (1994; Zbl 0822.65027)] and by \textit{R. Z. Ouedraogo, Y. Cherruault} and \textit{K. Abbaoui} [Kybernetes 29, 1298-1305 (2000; Zbl 0994.65054)]. The absolute convergence of the series giving the solution of the equation is proved under some constraints. Two numerical examples are presented which suggest that the method proposed here is more accurate than the methods from literature.
scientific article; zbMATH DE number 1861232