Review of the Numerical Analysis of the Quadratic Riccati Equation using Adomian Decomposition Methods and Taylor Expansion

Abstract

Riccati differential equations are a class of non-linear differential equations with numerous physical applications. In this research, we described a numerical method based on decomposition and compared the results to the exact solution. Riccati's differential equations have quadratic solutions expressed as an endless string using an iterative approach is introduced. The solutions of Riccati differential equations in the quadratic form are exhibited in terms of an infinite series, which are obtained by the iterative algorithm. We conducted comparisons between the exact and approximate solutions. The similarities between the Taylor series approach and the new method highlight the latter is simplicity and efficacy. We used tables and graphs by using MATLAB to show how similar the current method is to the exact solution. Keywords: Riccati, differential equations, an infinite series, MATLAB.