Journal of mathematics and computer science 14 (2015), 162-170 Modification of The HPM by Using Optimal Newton Interpolation Polynomial for Quadratic Riccati Differential Equation F. Ghomanjani 1,* , F. Divandar 2 1 Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran. 2 Department of Control, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran. * fatemeghomanjani@gmail.com Article history: Received November 2014 Accepted December 2014 Available online December 2014 Abstract In this work, an efficient modification of the homotopy analysis method by using optimal Newton interpolation polynomials is given for the approximate solutions of the Riccati differential equations. This presented method can be applied to linear and nonlinear models. Examples show that the method is effective. Keywords: quadratic Riccati differential equation, modification of the HPM, Newton interpolation. 1. Introduction Riccati differential equations are a class of nonlinear differential equations of much importance, and play a significant role in many fields of applied science [1]. The Riccati differential equation is named after the Italian nobleman Count Jacopo Francesco Riccati (1676-1754). The applications of this equation may be found not only in random processes, optimal control, and diffusion problems [2] but also in stochastic realization theory, optimal control, robust stabilization, network synthesis and financial mathematics. Solitary wave solutions of a nonlinear partial differential equation can be expressed as a polynomial in two elementary functions satisfying a projective Riccati equation [3]. Therefore, one has to go for numerical techniques or approximate approaches for getting its solution. Recently various iterative methods are employed for the numerical and analytical solution of functional equations such as Adomian's decomposition method (ADM) [4, 5], homotopy analysis method (HAM) [6], homotopy perturbation method (HPM) [7], variational iteration method (VIM) [8], and differential transform method (DTM) [9]. In [10], Liao has shown that HPM equations are equivalent to HAM equations when ћ= -1, and too, matrix differential transform method for solving of Riccati types matrix differential equations [11]. In this work, we introduce a new modification the HPM using optimal Newton interpolation polynomials. The schemes are tested for some examples. This study is organized as follows: In section 2, we present the standard HAM. In section 3, we present the modification technique of HAM. In section 4, the method is applied to a variety of examples to show efficiency and simplicity of the method.