LAUSR

In this study, an effective and rapidly convergent analytical technique is introduced to obtain approximate analytical solutions for nonlinear differential equations. The technique is a combination of the optimal quasilinearization method and the Picard iteration method. The optimal quasilinearization method is used to reduce the nonlinear differential equation to a sequence of linearized differential equations and the Picard iteration method is applied to get the approximate solutions of the linearized equations arising from the optimal quasilinearization method. The convergence analysis of the technique is also discussed. To determine the efficiency and effectiveness of the technique, we consider two numerical examples from real-world applications. The proposed method can easily be extended to a wide class of nonlinear differential equations also.