On Review of the Convergence Analyses of the Runge Kutta Fixed Point Iterative Methods | Asian Journ

Early in the nineteenth century, Runge Kutta, together with K. Heun and E. J. Nystrom, significantly developed and subsequently enlarged the so-called numerical techniques of solution for Ordinary Differential Equations of Various Orders. Work on the approach has never stopped since then. However, we examine and emphasise in this study that these approaches are not only a numerical way of solution, but also a very efficient iterative method. We describe all of the different Runge Kutta iterative techniques in part one, and their convergence in section two, while the convergence analysis was shown using numeric examples in section three, confirming that only consistent and stable iterative Runge Kutta methods are convergent. As a result, the goal of this study is to determine that no Runge Kutta technique can be regarded to be convergent unless it is consistent and stable.

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