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

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’

On some properties of the block linear multi-step methods

The convergence, stability and order of Block linear Multistep methods have been determined in the past based on individual members of the block. In this paper, methods are proposed to examine the properties of the entire block. Some Block Linear Multistep methods have been considered, their convergence, stability and order have been determined using these approaches. Keywords: Annuity, Amortisation, Sinking Fund, Present and Future Value Annuity, Maturity date and Redemption value