Hybrid Block Method for the Solution of Nonlinear Systems of First-order Ordinary Differential Equations

It is a known fact that systems of nonlinear ordinary differential equations have been known to be tedious to solve. In fact, some of the systems of nonlinear differential equations do not have closed form (exact) solutions. In view of the foregoing, this research is motivated by the need to derive a hybrid block method within a three-step integration interval   3 , n n x x for the solution of nonlinear system of equations. The formulation of the method was carried out via interpolation and collocation technique. The power series polynomial was adopted as basis function in deriving the method. Three off-grid points were carefully inserted within the three-step interval in order to guarantee a zerostable method. The basic properties of the method were further analyzed. The results obtained showed that the method performed better than the ones results were compared with. The method is also efficient and computationally reliable.