A Class of Block Multi-Step Methods for the Solutions of Ordinary Differential Equation (Ode)

In this research, an attempt is made to derive a self starting block procedure for some K-step linear multi-step methods (for K=1, 2 and 3), using Chebyshev polynomial as the basis function. The continuous interpolant were derived and collocated at grid and off-grid points to give the discrete methods used in block and applied simultaneously for the solution of non stiff initial value problem.The regions of absolute stability of the methods are plotted and are shown to be A (α) stable. The methods for K=2 and K=3 were experimented on initial value problems and the results reveal that the newly constructed block methods have good error stability and are efficient.