Phase space analysis in numerical integration of ordinary differential equations

1974 ◽  
pp. 107-127
Author(s):  
Bernard E. Howard
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Integration ◽  
Phase Space Analysis ◽  
Space Analysis

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.

Phase-space analysis of daily streamflow: characterization and prediction

1998 ◽  
Vol 21 (6) ◽  
pp. 463-475 ◽  
Author(s):  
Q. Liu ◽  
S. Islam ◽  
I. Rodriguez-Iturbe ◽  
Y. Le
Keyword(s):  
Phase Space ◽  
Phase Space Analysis ◽  
Space Analysis ◽  
Daily Streamflow

Phase space analysis of convection in a 3He-superfluid 4He solution

1983 ◽  
Vol 7 (1-3) ◽  
pp. 69-72 ◽  
Author(s):  
Hans Haucke ◽  
Yoshiteru Maeno
Keyword(s):  
Phase Space ◽  
Superfluid 4He ◽  
Phase Space Analysis ◽  
Space Analysis

scholarly journals Quantum phase-space analysis of the pendular cavity

2004 ◽  
Vol 70 (4) ◽  
Author(s):  
M. K. Olsen ◽  
A. B. Melo ◽  
K. Dechoum ◽  
A. Z. Khoury
Keyword(s):  
Phase Space ◽  
Quantum Phase ◽  
Phase Space Analysis ◽  
Space Analysis
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