Análisis del comportamiento del error global en los métodos explícitos de Runge-Kutta

Abstract

Initial value solvers typically input a problem specification and an error tolerance and output an approximate solution. However, obtaining precise and reliable numerical solutions requires knowledge of the allowable spacing between mesh nodes. Also, it is necessary to carry out global error control. Therefore, the aim of the present work is to analyze the behavior of the global error in explicit Runge-Kutta methods, determine the order of the global error and obtain the necessary condition to guarantee convergence.