The divergence of Hansen-Sengupta method applied on Trapezoidal - Newton operator for nonlinear interval system of equations

Abstract

The Hansen-Sengupta operator is discussed in the light of circular interval arithmetic for the algebraic inclusion of zeros of nonlinear interval systems of equations which is known to be efficient for handling such problems. It was the aim of this paper to extend such good convergence behavior possessed by Hansen-Sengupta operator on the well known Trapezoidal-Newton functional iterative method. It was discovered that the Hansen-Sengupta method applied on Trapezoidal-Newton method will produce not only overestimated results but also results that are not finitely bounded. This was demonstrated by numerical example wherein we compared notes with results obtained from Uwamusi [16] and concluded that Hansen-Sengupta method applied on the Trapezoidal-Newton method indeed, diverges.

Keywords: interval nonlinear systems of equations, Hansen –Sengupta operator, Trapezoidal-Newton method, circular interval arithmetic

Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 107 – 114