_________ *Corresponding author’s e-mail: norizarina@usim-edu.my ASM Sc. J., 13, 2020 https://doi.org/10.32802/asmscj.2020.sm26(4.8) Numerical Approximation of Riccati Type Differential Equations Ahmad Fadly Nurullah bin Rasedee 1 , Mohamad Hasan Abdul Sathar 2 , Norizarina Ishak 3* , Siti Raihana Hamzah 3 and Nur Amalina Jamaludin 4 1 Faculty of Economics and Muamalat, Universiti Sains Islam Malaysia, 71800 Bandar Baru Nilai, Negeri Sembilan, Malaysia. 2 Centre of Foundation Studies for Agricultural Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia. 3 Faculty of Science and Technology, Universiti Sains Islam Malaysia, 71800 Bandar Baru Nilai, Negeri Sembilan, Malaysia. 4 Centre for Defence Foundation Studies, Universiti Pertahanan Nasional Malaysia, Selangor, Malaysia. Riccati differential equations are one of the most common type of non-linear differential equation used to model real life applications from various fields. The issue when dealing with non-linear differential equations is obtaining their exact solutions. In this research, a three-point block multi-step method in backward difference form is introduced to provide approximated solutions for these Riccati differential equations. The accuracy of the proposed three-point block method will be tested against known numerical methods. The efficiency of the method will apparent when compared with another multi-step method. Keywords: Riccati equations, Block method, ODEs I. INTRODUCTION Applications of Riccati differential equations have become a common occurrence in social and natural sciences. Mathematical models in the form of Riccati differential equations ranges from stochastic realization theory, financial mathematics, network synthesis to random process and diffusion problems. The general Riccati differential equation (RDE) has the form 2 0 () ()() () () ( ), , yt tyt ty t t t t T     = + +   ( ) 0 yt C = where the functions ( ), t  () t  and () t  are given. Direct approach using multistep method have become a trend for solving higher order ordinary differential equations. This is because compared to reduction of order methods, direct methods have shown to be not only accurate but with the added advantage of being cost effective (computational cost). Previous approximation methods for ODEs were considered to be robust because of their efficiency but, due to authors such as Krogh (1973), Lambert (1973) and Suleiman (1989) the interest of researchers was revived. Among the more avid researchers in developing these direct methods includes authors such as Suleiman (2011), Rasedee et. al., (2016) and Ijamet al. (2018). In the current work, a three-point block multistep method is introduced to obtain the numerical approximation for Riccati differential equations. Inspired by research conducted in Suleiman (1989), the three-point block method is infused with a variable order step size algorithm (3PBVOS) to reduce computational cost. The 3PBVOS method is formulated using an Adams-like code to