On Review of the Convergence Analyses of the Runge Kutta Fixed Point Iterative Methods | Asian Journal of Pure and Applied Mathematics

Runge Kutta alongside K. Heun and E. J. Nystrom early in the nineteenth century extensively developed and consequently expanded the so called numerical methods of solution for the Ordinary Differential equations of various orders. Since then, work on the method has never ceased. However in this paper, we review and make stronger the fact that these methods are not only just a numeric method of solution but a very efficient iterative method. We outline in section one all the various Runge Kutta iterative methods and in section two their convergence while in section 3, the convergence analysis was illustrated with numeric examples which confirmed that only consistent and stable iterative Runge Kutta methods are convergent. Hence the objective of this research work is to establish that every Runge Kutta method which is not consistent and stable cannot be said to be convergent.

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