Solving Riccati differential equation using Fourier polynomial basis

Abstract

A new matrix method based on polynomial approximation, using complex Fourier polynomial basis is presented for the solution of Riccati differential equations (RDE). The proposed method converts the governing differential equation of the system into a matrix equation, which corresponds to a system of nonlinear algebraic equations with unknown coefficients. The solution is calculated in the form of a series with easily computable components. Some numerical examples are included to demonstrate the validity and applicability of the technique.