Pseudospectral methods for nonlinear pendulum equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 1, pp. 79-84.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article searched on mathematics and numerical solutions for the nonlinear pendulum (Chaotic pendulum). The numerical solution that was used for our research suitably the pseudospectral methods. With these equations, we studied and calculated on the interval $[-1, 1]$, with boundary conditions already known. We used the software Mathematica 10.4 to calculate the results of the problems.
Keywords: chaotic pendulum, Chebyshev, pseudospectral methods, differentiation matrices, collocation method, nonlinear equations.
@article{JSFU_2019_12_1_a6,
     author = {Le Anh Nhat},
     title = {Pseudospectral methods for nonlinear pendulum equations},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {79--84},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_1_a6/}
}
TY  - JOUR
AU  - Le Anh Nhat
TI  - Pseudospectral methods for nonlinear pendulum equations
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2019
SP  - 79
EP  - 84
VL  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2019_12_1_a6/
LA  - en
ID  - JSFU_2019_12_1_a6
ER  - 
%0 Journal Article
%A Le Anh Nhat
%T Pseudospectral methods for nonlinear pendulum equations
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2019
%P 79-84
%V 12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2019_12_1_a6/
%G en
%F JSFU_2019_12_1_a6
Le Anh Nhat. Pseudospectral methods for nonlinear pendulum equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 1, pp. 79-84. http://geodesic.mathdoc.fr/item/JSFU_2019_12_1_a6/

[1] A. Belendez, E. Arribas, “Approximate solutions for the nonlinear pendulum equation using a rational harmonic representation”, Computers $\$ Mathematics with Applications, 64:9 (2012), 1602–1611 | DOI | MR | Zbl

[2] G. Moshe, The Chaotic Pendulum, World Scientific Publishing Co. Pte. Ltd, 2010 | Zbl

[3] G.L. Baker, J.A. Blackburn, The Pendulum — a case study in physics, Oxford University Press Inc., New York, 2005 | MR | Zbl

[4] J.C. Mason, D.C. Handscomb, Chebyshev Polynomials, CRC Press LLC, 2003 | MR | Zbl

[5] W.S. Don, A. Solomonoff, “Accuracy and speed in computing the Chebyshev collocation devivative”, SIAM Juarnal of Scientific Computing, 16:6 (1991), 1253–1268 | DOI | MR