scholarly journals Convergence Acceleration Algorithm via an Equation Related to the Lattice Boussinesq Equation

2011 ◽  
Vol 33 (3) ◽  
pp. 1234-1245 ◽  
Author(s):  
Yi He ◽  
Xing-Biao Hu ◽  
Jian-Qing Sun ◽  
Ernst Joachim Weniger
Keyword(s):  
Boussinesq Equation ◽  
Convergence Acceleration ◽  
Convergence Acceleration Algorithm

A new method to generate non-autonomous discrete integrable systems via convergence acceleration algorithms

2015 ◽  
Vol 27 (2) ◽  
pp. 194-212 ◽  
Author(s):  
YI HE ◽  
XING-BIAO HU ◽  
HON-WAH TAM ◽  
YING-NAN ZHANG
Keyword(s):  
Integrable Systems ◽  
Numerical Experiments ◽  
Boussinesq Equation ◽  
Volterra Equation ◽  
Algebraic Method ◽  
Convergence Acceleration ◽  
New Method ◽  
Discrete Integrable Systems ◽  
Convergence Acceleration Algorithm ◽  
Autonomous Version

In this paper, we propose a new algebraic method to construct non-autonomous discrete integrable systems. The method starts from constructing generalizations of convergence acceleration algorithms related to discrete integrable systems. Then the non-autonomous version of the corresponding integrable systems are derived. The molecule solutions of the systems are also obtained. As an example of the application of the method, we propose a generalization of the multistep ϵ-algorithm, and then derive a non-autonomous discrete extended Lotka–Volterra equation. Since the convergence acceleration algorithm from the lattice Boussinesq equation is just a particular case of the multistep ϵ-algorithm, we have therefore arrived at a generalization of this algorithm. Finally, numerical experiments on the new algorithm are presented.

Couette Flow Profiles for Two Nonclassical Taylor-Couette Cells

2000 ◽  
Vol 122 (2) ◽  
pp. 435-438
Author(s):  
Michael C. Wendl ◽  
Ramesh K. Agarwal
Keyword(s):  
High Resolution ◽  
Exact Solutions ◽  
Numerical Simulations ◽  
Couette Flow ◽  
Convergence Rates ◽  
Initial Conditions ◽  
Convergence Acceleration ◽  
Flow Profiles ◽  
Convergence Acceleration Algorithm ◽  
Taylor Couette

Exact solutions for the Couette profile in two nonclassical Taylor-Couette cells are reported. The profiles take the form of eigenfunction expansions, whose convergence rates can be significantly accelerated using a representative convergence acceleration algorithm. Results are thus suitable as initial conditions for high resolution numerical simulations of transition phenomena in these configurations. [S0098-2202(00)02602-X]

CONVERGENCE ACCELERATION OF INTEGRAL TRANSFORM SOLUTIONS

2001 ◽  
Vol 3 (1) ◽  
pp. 6
Author(s):  
Mikhail D. Mikhailov ◽  
Renato M. Cotta
Keyword(s):  
Integral Transform ◽  
Convergence Acceleration
Sign in / Sign up

Export Citation Format

Share Document