Three quarter - step block hybrid algorithm for the numerical solution of first order initial value problems of ordinary differential equations

Attracted by the important role of ordinary differential equations in many physical situations like engineering, control theory, biological, and economics, a three quarter - step block hybrid algorithm is constructed for the purpose of solving first-order initial value problems of ordinary differential equations (FIVPODEs). Our approach leverages on off grid points other than the usual whole step point methods constructed by many researchers; this is viewed as an important shift from the usual norm. Some of the advantages of hybrid methods is that they possess remarkably small error constants as observed in Table I among other advantages. Some problems solved by some existing methods are also solved using the constructed algorithm to demonstrate the simplicity, validity and applicability of the method. The results obtained revealed that the method is suitable for all forms of first-order initial value problems be it linear or non-linear ordinary differential equations.