In this paper, block implicit one-step method of order seven is proposed for the numerical integration of first order initial value problems. The method is based on collocation of the differential system and interpolation of the approximate at the grid and off-grid points. The procedure yields six consistent finite difference schemes which are combined as simultaneous numerical integrators to form block method. The method is found to be zero-stable hence convergent. The accuracy of the method is tested with some standard first order initial value problems. The results show a better performance over the existing methods
Keywords: Block, Finite Differential Schemes, Implicit, Simultaneous Numerical Integrators, Zero-Stable And Convergent.
