Error Propagation in the RK5GL3 Method
نویسنده
چکیده
The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe the propagation of local errors in this method, and show that the global order of RK5GL3 is expected to be six, one better than the underlying RungeKutta method. Keywords—RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, order, local error, global error.
منابع مشابه
Local Error Control in the RK5GL3 Method
The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a ...
متن کاملThe Effects of Illuminants and Standard Observers Combination on Relationship between Spectrophotometric Error and Colorimetric Inaccuracy
The colorimetric error depends on the spectrophotometric inaccuracy. In this paper, a new method is introduced for determining the relationship between spectrophotometric error and colorimetric inaccuracy. The error propagation in colorimetric parameter calculation is evaluated using a linear relation between variance of reflectance spectra and CIE tristimulus values. This linear formula ca...
متن کاملSignificant Error Propagation in the Finite Difference Solution of Non-Linear Magnetostatic Problems Utilizing Boundary Condition of the Third Kind
This paper poses two magnetostatic problems in cylindrical coordinates with different permeabilities for each region. In the first problem the boundary condition of the second kind is used while in the second one, the boundary condition of the third kind is utilized. These problems are solved using the finite element and finite difference methods. In second problem, the results of the finite di...
متن کاملآموزش شبکه عصبی MLP در فشردهسازی تصاویر با استفاده از روش GSA
Image compression is one of the important research fields in image processing. Up to now, different methods are presented for image compression. Neural network is one of these methods that has represented its good performance in many applications. The usual method in training of neural networks is error back propagation method that its drawbacks are late convergence and stopping in points of lo...
متن کاملModeling of measurement error in refractive index determination of fuel cell using neural network and genetic algorithm
Abstract: In this paper, a method for determination of refractive index in membrane of fuel cell on basis of three-longitudinal-mode laser heterodyne interferometer is presented. The optical path difference between the target and reference paths is fixed and phase shift is then calculated in terms of refractive index shift. The measurement accuracy of this system is limited by nonlinearity erro...
متن کامل