A New Super Convergent Implicit Runge-Kutta Method for First Order Ordinary Differential Equations

We present a new efficient super convergent implicit Runge-kutta method (RKM) for solving differential equations (ODEs). Chybechev’s polynomial is used as basis function. Collocation and Matrix inversion method is used to derive our continuous schemes. The continuous formula is evaluated at zeros of the first Chybechev’s polynomial to give us Runge-kutta evaluation functions for the direct iteration of our solutions. Experimental examples used show that the method is A stable, highly efficient, has simple coefficients, less implementation cost when compared with similar methods in the literature