A new efficient method for solving quadratic Riccati differential equation

Belal Batiha

doi:10.14419/ijamr.v4i1.4113

Abstract

A new efficient method called the multistage variational iteration method (MVIM) is applied to the solution of quadratic Riccati differential equations. A comparison between MVIM solution with classical variational iteration method (VIM) and exact solution has been made and show that the MVIM is a powerful method to the solution of nonlinear differential equations.

Highlights

The Riccati differential equation is named after the Italian nobleman Count Jacopo Francesco Riccati (1676– 1754)
A comparison between multistage variational iteration method (MVIM) solution with classical variational iteration method (VIM) and exact solution has been made and show that the MVIM is a powerful method to the solution of nonlinear differential equations
Multistage variational iteration method or MVIM was first introduced by Batiha et al [28] on a class of nonlinear system of ordinary differential equations

Summary

Introduction

The Riccati differential equation is named after the Italian nobleman Count Jacopo Francesco Riccati (1676– 1754). Geng [7] presented a modified variational iteration method to solve quadratic Riccati equation. He [9] solved the classical Blasius’ equation using VIM He [10] gave a solution for seepage flow with fractional derivatives in porous media using VIM. He [12] used VIM to solve autonomous ordinary differential systems He [13] coupled the iteration method with the perturbation method to solve the well-known Blasius equation. Abbasbandy [26] solved the quadratic Riccati differential equation by He’s variational iteration method with considering Adomian’s polynomials. We shall investigate VIM and MVIM accuracy for a longer time frame to show its reliability to Riccati equation

Variational iteration method

Analysis of Riccati differential equation

Numerical results and discussion

Conclusions