Q-difference and confluent forms of the lattice Boussinesq equation and the relevant convergence acceleration algorithms

2011 ◽  
Vol 52 (2) ◽  
pp. 023522 ◽  
Author(s):  
Jian-Qing Sun ◽  
Yi He ◽  
Xing-Biao Hu ◽  
Hon-Wah Tam
Keyword(s):  
Boussinesq Equation ◽  
Convergence Acceleration

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.

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

scholarly journals Analytical mathematical schemes: Circular rod grounded via transverse Poisson’s effect and extensive wave propagation on the surface of water

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 545-554
Author(s):  
Asghar Ali ◽  
Aly R. Seadawy ◽  
Dumitru Baleanu
Keyword(s):  
Wave Propagation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Longitudinal Wave ◽  
Symbolic Computation ◽  
Boussinesq Equation ◽  
Nonlinear Partial Differential Equations ◽  
Wave Model ◽  
Simple Equation ◽  
Partial Differential

AbstractThis article scrutinizes the efficacy of analytical mathematical schemes, improved simple equation and exp(-\text{Ψ}(\xi ))-expansion techniques for solving the well-known nonlinear partial differential equations. A longitudinal wave model is used for the description of the dispersion in the circular rod grounded via transverse Poisson’s effect; similarly, the Boussinesq equation is used for extensive wave propagation on the surface of water. Many other such types of equations are also solved with these techniques. Hence, our methods appear easier and faster via symbolic computation.

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