A multistage successive approximation method for Riccati differential equations

Abstract

Riccati differential equations have played important roles in the theory and practice of control systems engineering. Our goal in this paper is to propose a new multistage successive approximation method for solving Riccati differential equations. The multistage successive approximation method is derived from an existing piecewise variational iteration method for solving Riccati differential equations. The multistage successive approximation method is simpler in terms of computing implementation in comparison with the existing piecewise variational iteration method. Computational tests show that the order of accuracy of the multistage successive approximation method can be made higher by simply taking more number of successive iterations in the multistage evolution. Furthermore, taking small size of each subinterval and taking large number of iterations in the multistage evolution lead that our proposed method produces small error and becomes high order accurate.

Shifted Legendre method for solutions of Riccati type functional differential equations and application of RL circuit model

“…It is known that control systems engineering plays an important role in electrical engineering and related fields. [3][4][5] For this reason, it is important to find the exact solution of the equation. However, in view of the nonlinear nature of the equations, it is unlikely that such exact solutions will be found.…”

“…Riccati differential equations emerge in the solution of the Schrödinger equation, which is one of the important equations of mathematical physics, and also in control systems engineering. It is known that control systems engineering plays an important role in electrical engineering and related fields 3–5 . For this reason, it is important to find the exact solution of the equation.…”

A numerical-analytical iterative method for solving an electrical oscillator equation

“…Readers interested in the modelling of the van der Pol equation can consult the literature [29]- [33]. The standard successive approximation method is able to TELKOMNIKA Telecommun Comput El Control  A numerical-analytical iterative method for solving an electrical oscillator equation (Sudi Mungkasi) 1219 solve the problem only for temporal points close enough to the initial time, unless a large number of iterations are taken in the successive approximations [34]. However, taking a large number of successive iterations is impractical and should be avoided, because of the expensive computation.…”