Four Points Block Method with Second Derivative for Solving First Order Ordinary Differential Equations

In this study, we devised 4-point implicit block (New 4pb) approaches that take advantage of second derivatives. The aim provides is more accurate and quicker numerical solutions to first - order ordinary differential equations (ODEs). Whereas the properties of the (New 4pb) method such as the  order and zero-stability have been discussed. After that, the approaches are applied to a collection of first-order (ODEs). In addressing the set of test problems, numerical results clearly indicate that the newly proposed systems outperformed previous, well-known existing methods.