scholarly journals Study of the spectral stability of generalized Runge-Kutta methods applied to numerical integration of the initial-bounary value problem for the transport equation

2014 ◽  
Vol 7 (3) ◽  
pp. 279-294 ◽  
Author(s):  
V.P. Matveenko
Keyword(s):  
Transport Equation ◽  
Numerical Integration ◽  
Spectral Stability ◽  
Runge Kutta

scholarly journals Enhancing Accuracy of Runge–Kutta-Type Collocation Methods for Solving ODEs

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 174
Author(s):  
Janez Urevc ◽  
Miroslav Halilovič
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Integration ◽  
Integral Form ◽  
Collocation Methods ◽  
Nonlinear Odes ◽  
New Class ◽  
New Methods ◽  
Runge Kutta

In this paper, a new class of Runge–Kutta-type collocation methods for the numerical integration of ordinary differential equations (ODEs) is presented. Its derivation is based on the integral form of the differential equation. The approach enables enhancing the accuracy of the established collocation Runge–Kutta methods while retaining the same number of stages. We demonstrate that, with the proposed approach, the Gauss–Legendre and Lobatto IIIA methods can be derived and that their accuracy can be improved for the same number of method coefficients. We expressed the methods in the form of tables similar to Butcher tableaus. The performance of the new methods is investigated on some well-known stiff, oscillatory, and nonlinear ODEs from the literature.

Advances in the Numerical Integration of the Three-Dimensional Euler Equations in Vibrating Cascades

1993 ◽  
Vol 115 (4) ◽  
pp. 781-790 ◽  
Author(s):  
G. A. Gerolymos
Keyword(s):  
Boundary Conditions ◽  
Numerical Integration ◽  
Euler Equations ◽  
Finite Volume ◽  
Three Dimensional ◽  
Computational Results ◽  
Grid Refinement ◽  
Mobile Grid ◽  
Transonic Compressor ◽  
Runge Kutta

In the present work an algorithm for the numerical integration of the three-dimensional unsteady Euler equations in vibrating transonic compressor cascades is described. The equations are discretized in finite-volume formulation in a mobile grid using isoparametric brick elements. They are integrated in time using Runge-Kutta schemes. A thorough discussion of the boundary conditions used and of their influence on results is undertaken. The influence of grid refinement on computational results is examined. Unsteady convergence of results is discussed.

scholarly journals On the numerical integration of orthogonal flows with Runge–Kutta methods

2000 ◽  
Vol 115 (1-2) ◽  
pp. 121-135 ◽  
Author(s):  
M. Calvo ◽  
M.P. Laburta ◽  
J.I. Montijano ◽  
L. Rández
Keyword(s):  
Numerical Integration ◽  
Runge Kutta
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