A Class of Continuous Implicit Seventh-eight method for solving y’= f(x, y) using power series

Abstract

In this article, we develop a continuous implicit seventh-eight method using interpolation and collocation of the approximate solution for the solution of y’ = f(x,y) with a constant step-size. The method uses power series as the approximate solution in the derivation of the method. The independent solution was then derived by adopting block integrator. The properties of the method was investigated and found to be zero stable, consistent and convergent. The integrator was tested on numerical examples ranging from linear problem, Prothero-Robinson Oscillatory problem, Growth Model and Sir Model. The results show that the computed solution is closer to the exact solution and also, the absolutes errors are minimal and uses lesser time for the computations.