AN ORDER EIGHT GAUSS QUADRATURE RUNGE – KUTA METHOD FOR ORDINARY DIFFERENTIAL EQUATIONS (ODEs)

Abstract

We present a strong convergence implicit Runge-Kutta method, with four stages, for solution of initial value problem of first ordinary differential equations. Collocation method is used to derive a continuous scheme which evaluated at special points, the Gaussian points of fourth degree Legendre polynomial, gives us four functional evaluations in the Runge-Kutta method for the iteration of the solutions. Convergent property of the method is discussed. Experimental problems used to check the quality of the scheme show that the method is highly efficient, A – stable, has simple structure, converges to exact solution faster and better than some existing popular methods cited in this paper.