A higher order frozen Jacobian iterative method for solving Hamilton-Jacobi equations

作者：Alzahrani Ebraheem O; Al Aidarous Eman S; Younas Arshad M M; Ahmad Fayyaz^*; Ahmad Shamshad; Ahmad Shahid

来源：Journal of Nonlinear Sciences and Applications, 2016, 9(12): 6210-6227.

DOI：10.22436/jnsa.009.12.26

• Hamilton-Jacobi equations
• frozen Jacobian iterative methods
• systems of nonlinear equations
• Chebyshev pseudo-spectral collocation method

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.

• 出版日期2016