Some implementation schemes for implicit Runge-Kutta methods

1980 ◽  
pp. 12-24 ◽  
Author(s):  
J. C. Butcher
Keyword(s):  
Runge Kutta

Semi-implicit Runge-Kutta schemes for stiff multi-dimensional reacting flows

1997 ◽  
Author(s):  
Jack Yoh ◽  
Xiaolin Zhong ◽  
Jack Yoh ◽  
Xiaolin Zhong
Keyword(s):  
Reacting Flows ◽  
Runge Kutta

Modelación, Simulación y Control de Aerogeneradores con Generador de Inducción Doblemente Alimentado Utilizando Matlab

2015 ◽  
Vol 11 (1) ◽  
Author(s):  
W. Vásquez ◽  
J. Játiva
Keyword(s):  
Runge Kutta

En este trabajo se presenta la modelación de los componentes aerodinámicos, mecánicos, eléctricos y de control del aerogenerador con generador de inducción doblemente alimentado (DFIG). La modelación es empleada para crear un programa en el software Matlab. Se utiliza el método de Runge Kutta de cuarto orden para solucionar las ecuaciones diferenciales existentes en la modelación. La estrategia de control del convertidor PWM bidireccional se base en la técnica de control vectorial que emplea marcos de referencia giratorios, la cual permite el control de las potencias activa y reactiva producidas por el DFIG. Se describe el proceso de inicialización del sistema aerogenerador con DFIG, para obtener las condiciones de estado estable antes de iniciar la simulación. Se analiza el comportamiento del aerogenerador con DFIG ante cambios de la velocidad del viento y fallas de corto circuito. Los resultados finales muestran que la potencia activa del DFIG varía de acuerdo al comportamiento de la velocidad del viento, mientras que la potencia reactiva permanece casi invariante. Los resultados obtenidos son comparados con los resultados del modelo del aerogenerador con DFIG existente en Simulink de Matlab.

scholarly journals Krylov SSP Integrating Factor Runge–Kutta WENO Methods

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1483
Author(s):  
Shanqin Chen
Keyword(s):  
Large Time ◽  
Hyperbolic Equations ◽  
Strong Stability ◽  
Matrix Exponential ◽  
Linear Component ◽  
Nonlinear Hyperbolic Equations ◽  
Time Step ◽  
Integrating Factor ◽  
The Matrix ◽  
Runge Kutta

Weighted essentially non-oscillatory (WENO) methods are especially efficient for numerically solving nonlinear hyperbolic equations. In order to achieve strong stability and large time-steps, strong stability preserving (SSP) integrating factor (IF) methods were designed in the literature, but the methods there were only for one-dimensional (1D) problems that have a stiff linear component and a non-stiff nonlinear component. In this paper, we extend WENO methods with large time-stepping SSP integrating factor Runge–Kutta time discretization to solve general nonlinear two-dimensional (2D) problems by a splitting method. How to evaluate the matrix exponential operator efficiently is a tremendous challenge when we apply IF temporal discretization for PDEs on high spatial dimensions. In this work, the matrix exponential computation is approximated through the Krylov subspace projection method. Numerical examples are shown to demonstrate the accuracy and large time-step size of the present method.

scholarly journals A Neural Network Technique for the Derivation of Runge-Kutta Pairs Adjusted for Scalar Autonomous Problems

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1842
Author(s):  
Vladislav N. Kovalnogov ◽  
Ruslan V. Fedorov ◽  
Yuri A. Khakhalev ◽  
Theodore E. Simos ◽  
Charalampos Tsitouras
Keyword(s):  
Neural Network ◽  
Differential Evolution ◽  
Initial Value Problem ◽  
Fitness Function ◽  
Initial Value ◽  
Runge Kutta

We consider the scalar autonomous initial value problem as solved by an explicit Runge-Kutta pair of orders 6 and 5. We focus on an efficient family of such pairs, which were studied extensively in previous decades. This family comes with 5 coefficients that one is able to select arbitrarily. We set, as a fitness function, a certain measure, which is evaluated after running the pair in a couple of relevant problems. Thus, we may adjust the coefficients of the pair, minimizing this fitness function using the differential evolution technique. We conclude with a method (i.e. a Runge-Kutta pair) which outperforms other pairs of the same two orders in a variety of scalar autonomous problems.

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