Akbari–Ganji's Method - Dilleswar Rao, Tharasi; Mahato, Nisha; Karunakar, Perumandla; Chakraverty, Snehashish (Advanced Numerical and Semi-Analytical Methods for Differential Equations, 2019)
Modeling of nonlinear differential equations analytically is rather more difficult compared to solving linear differential equations. In this regard, the Akbari‐lGanji's method (AGM) may be considered as a powerful algebraic (semi‐analytic) approach for solving such problems. In the AGM, initially a solution function consisting of unknown constant coefficients is assumed satisfying the differential equation and the initial conditions (IC). Then, the unknown coefficients are computed using algebraic equations obtained with respect to IC and their derivatives. This chapter illustrates the basic notion of nonlinear differential equation and its solution procedure. It presents the detailed illustration of the AGM approach for solving second‐order unforced and forced nonlinear ordinary differential equations. The chapter also illustrates the efficiency of the procedure using unforced and forced nonlinear differential equations with respect to Helmholtz and Duffing equations, respectively.