A Method for Improving the Embedded Runge Kutta Fehlberg 4(5)
نویسنده
چکیده
In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.
منابع مشابه
Numerical Solution for Hybrid Fuzzy Differential Equations by Ruge-Kutta Fehlberg Method
In this paper we study numerical methods for Hybrid Fuzzy Differential equations by an appllication of the Runge-kutta Fehlberg method for fuzyy differential equations. We prove a convergence result and give numerical examples to illustrate the theory.
متن کاملAdaptive-Step-Size Numerical Methods in Rewriting-Logic-Based Formal Analysis of Interacting Hybrid Systems
This paper focuses on the formal modeling, simulation, and analysis of interacting hybrid systems that influence each other’s continuous behaviors. We define in the rewriting-logic-based Real-Time Maude tool a method for the numerical approximation of the continuous dynamics specified by ordinary differential equations. We adapt the Runge-Kutta-Fehlberg 4/5 method to define an adaptive-step-siz...
متن کاملBandlimited implicit Runge–Kutta integration for Astrodynamics
We describe a new method for numerical integration, dubbed bandlimited collocation implicit Runge–Kutta (BLC-IRK), and compare its efficiency in propagating orbits to existing techniques commonly used in Astrodynamics. The BLC-IRK scheme uses generalized Gaussian quadratures for bandlimited functions. This new method allows us to use significantly fewer force function evaluations than explicit ...
متن کاملSome Practical Runge-Kutta Formulas*
A new selection is made of the most practical of the many explicit Runge-Kutta formulas of order 4 which have been proposed. A new formula is considered, formulas are modified to improve their quality and efficiency in agreement with improved understanding of the issues, and formulas are derived which permit interpolation. It is possible to do a lot better than the pair of Fehlberg currently re...
متن کامل