Block implicit algorithms for the solution of system of first order ordinary differential equations

A linear multi-step method (LMM) with continuous coefficient is considered in this paper and applied to solve system of first order ordinary differential equations of the form ý = f(x,y) and ź = g (x,y). All the implicit algorithms derived were of the uniform order 8 and zero-stable which are combined as simultaneous numerical integrators to provide solutions to system of first order initial value problems over sub-intervals which do not overlaps. The superiority of the method is demonstrated on both system of linear and non linear first order ODEs numerically.