On the solution of the Riccati equation by the Taylor matrix method

摘要

In this paper, we suggest a matrix method to solve the Riccati differential equation in terms of Taylor polynomials. This method is based on first taking the truncated Taylor series of the function in equations and then substituting their matrix forms into the given equation. Hence, the result matrix equation can be solved and the unknown Taylor coefficients can be found approximately. The solution is calculated in the form of a series with easily computable components. The numerical results show the effectiveness of the method for this type of equation. Comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate.