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We present implicit Runge-Kutta method using cosine functions for solving first order ordinary differential equations. Cosine functions are used to obtain special points which are used to construct the high order implicit Runge-Kutta methods. Collocation approach at these special points are used to generate continuous schemes for the generation of discrete schemes. The discrete schemes are reformulated to Runge-Kutta function-evaluations for solution of first order ordinary differential equations. Numerical experiments are used to show that the method are more efficient, simpler and convergent to exact solutions faster and better than exiting methods.
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