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Abstract
Due to severe step size restriction, it becomes absolutely necessary that only methods with large regions of absolute stability remain suitable for stiff equations. In this paper, the continuous Block one-step embedded numerical integrator of order 4 and order 5 have been constructed. The continuous scheme was evaluated at different points to obtain discrete schemes. The order, error constant, zero stability and consistency of the resulting discrete schemes were ascertained. The region of absolute stability of the block hybrid scheme was plotted. Their accuracy and stability investigated shows that the new methods are A(α)- stable, a property desirable of numerical methods suitable for the solutions of stiff ODE’s. The new one-step embedded Numerical Integrators used in block form tested on stiff systems of Ordinary Differential Equations confirms that they are efficient and they compare favorably with exact solution and the state of the art Matlab ODE solver, ode15s. (ode 15s is for stiff problems while ode 45s are for non-stiff problems)