ANALISIS HUBUNGAN ANTARA PERSAMAAN RICCATI DAN PERSAMAAN INTEGRAL VOLTERRA TIPE DUA

Abstract

In this paper, a method for finding solution of the Riccati equation is introduced. The Riccatiequation is the first order inhomogeneous nonlinear ordinary differential equation (ODE) that can always be transformed into a second order homogeneous linear ODE. Since, every initial value problem (IVP) of the second order linear ODEs can be transformed into a Volterra integral equation (IE) of the second type, evaluate this equation by approximate technique by means, the approximate solution of the Riccati equation can be found. The approximate technique of the Voterra IE has been describe before, is based on the Taylor series expansion and it’s modification of the method. Behind the Cramer’s rule, an approximate solution of the 2^nd type Volterra IE is easily can be determine and so, the approximate solution of the Riccati equation can be found. Test example is given to get conclusion about accuracy of the method.