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 2nd
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.
Keywords: Riccati equation,
2nd type Volterra
integral equation, approximate
solution, Taylor series
expansion, Cramer’s rule
Penulis: AnasKhairur Rijal,
Djuwandi, R. HeriSoelistyo U.
Kode Jurnal: jpmatematikadd140222
