An error embedded Runge-Kutta method for initial value problems
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In this paper, we propose an error embedded Runge-Kutta method to improvethe traditional embedded Runge-Kutta method. The proposed scheme can be applied intomost explicit embedded Runge-Kutta methods. At each integration step, the proposedmethod is comprised of two equations for the solution and the error, respectively. Thesesolution and error are obtained by solving an initial value problem whose solution hasthe information of the error at each integration step. The constructed algorithm controlsboth the error and the time step size simultaneously and possesses a good performancein the computational cost compared to the original method. For the assessment of theeffectiveness, the van der Pol equation and another one having a difficulty for the global
Abstract
In this paper, we propose an error embedded Runge-Kutta method to improvethe traditional embedded Runge-Kutta method. The proposed scheme can be applied intomost explicit embedded Runge-Kutta methods. At each integration step, the proposedmethod is comprised of two equations for the solution and the error, respectively. Thesesolution and error are obtained by solving an initial value problem whose solution hasthe information of the error at each integration step. The constructed algorithm controlsboth the error and the time step size simultaneously and possesses a good performancein the computational cost compared to the original method. For the assessment of theeffectiveness, the van der Pol equation and another one having a difficulty for the global
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