Título:
|
A higher order frozen Jacobian iterative method for solving Hamilton-Jacobi equations
|
Autor/a:
|
Alzahrani, Ebraheem O.; Alaidarous, Eman; Younas, Arshad M. M.; Ahmad, Fayyaz; Ahmad, Shamshad; Ahmad, Shahid
|
Otros autores:
|
Universitat Politècnica de Catalunya. GAA - Grup d'Astronomia i Astrofísica |
Abstract:
|
It is well-known that the solution of Hamilton-Jacobi equation may have singularity i.e., the solution is non-smooth or nearly non-smooth. We construct a frozen Jacobian multi-step iterative method for solving Hamilton-Jacobi equation under the assumption that the solution is nearly singular. The frozen Jacobian iterative methods are computationally very efficient because a single instance of the iterative method uses a single inversion (in the scene of LU factorization) of the frozen Jacobian. The multi-step part enhances the convergence order by solving lower and upper triangular systems. The convergence order of our proposed iterative method is 3(m-1) for m>=3. For attaining good numerical accuracy in the solution, we use Chebyshev pseudo-spectral collocation method. Some Hamilton-Jacobi equations are solved, and numerically obtained results show high accuracy. |
Abstract:
|
Peer Reviewed |
Materia(s):
|
-Hamilton-Jacobi equations -Hamilton-Jacobi equations -frozen Jacobian iterative methods -systems of nonlinear equations -Chebyshev pseudo-spectral collocation method -Equacions de Hamilton-Jacobi -Classificació AMS::49 Calculus of variations and optimal control; optimization::49L Hamilton-Jacobi theories, including dynamic programming |
Derechos:
|
|
Tipo de documento:
|
Artículo - Versión publicada Artículo |
Compartir:
|
|