A New Super Convergent Implicit Runge-Kutta Method for First Order Ordinary Differential Equations
Keywords:Super Convergence RKM, Chybechevâ€™s polynomial, Collocation and Matrix inversion method, Zeros of Chybechevâ€™s polynomial, A stable)
We present a new efficient super convergent implicit Runge-kutta method (RKM) for solving differential equations (ODEs). Chybechevâ€™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 Chybechevâ€™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.
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