New gaussian points for the solution of first order ordinary differential equations

Abstract

The Gauss Radau and the Lobatto points make use of the roots of the Legendre polynomial located within the step [-1,1]. In this paper, a new set of Gaussian points has been proposed and used as collocation points for the construction of block numerical methods for the solution of first order IVP through transformation within the step [Xn,Xn+2]. The new points resulted into stable numerical block methods of order 2m suitable for solving both stiff and non-stiff IVP. Numerical experiments carried out using the new Gaussian points revealed there efficiency on stiff differential equations. The results also reveal that methods using the new Gaussian points are more accurate than those using the standard Gaussian points on non-stiff initial value problems.

Keywords: Gaussian points, Collocation points, Legendre polynomial, Gauss,Lobatto, Block integrators, stiff and non-stiff IVP’s