The optimized decomposition method for a reliable treatment of IVPs for second order differential equations

Abstract

Abstract In this study, a general framework of the optimized decomposition method, which suggests an optimal construction of the series solutions, for analytic treatment of IVPs for second order differential equations is proposed. The presented framework expands the application of the method to several classes of IVPs for nonlinear differential equations. Illustrative comparisons between the optimized decomposition method and the Adomian decomposition method for solving some nonlinear IVPs is then presented. The results confirm that the optimized decomposition method produces better performance and gives better accuracy compared to Adomian decomposition method. The study highlights the strength and advantages of the method in dealing with nonlinear differential equations.