Second Derivative Two-step Block Hybrid Enright’s Linear Multistep Methods for Solving Initial Value Problems of General Second Order Stiff Ordinary Differential Equations

In this research, the formation of second derivative two-step block hybrid Enright’s linear multistep methods for solving initial value problems is studied. In forming the method, we follow Enright’s 1974 approach, by introducing the off-mesh points at both interpolation and collocations; we developed the continuous schemes for new Enright’s method. The analysis of new Enright method was studied and it was found to be consistent, convergent and zero-stable. We further computed the order, error constants and plotted the region of absolute stability within which the method is A-stable. The methods exhibited better accuracy level when provided with numerical examples than the existing method with which we compared our results.