One-third Hybrid Algorithm for Numerical solution of First-order Models Problems with Initial Condition

The collocation and interpolation technique on the power series approximate solution was used to develop a new continuous implicit hybrid one-third step method capable of solving first-order stiff initial value problems. This method has the advantage of allowing for easy step length changes and function evaluation at off-step points. The block method used to implement the main method ensures that each discrete method resulting from the block's simultaneous solution has the same order of accuracy as the main method. The method provides large intervals of absolute stability; it is consistent, zero stable, and thus converges. Sample examples of linear and nonlinear stiff problems were used to evaluate the method's performance. When compared to other existing methods, our developed method has been shown to be more accurate.