TY - JOUR AU - Alzahrani, Ebraheem O. AU - Al-Aidarous, Eman S. AU - Younas, Arshad M. M. AU - Ahmad, Fayyaz AU - Ahmad, Shamshad AU - Ahmad, Shahid PY - 2016 TI - A higher order frozen Jacobian iterative method for solving Hamilton-Jacobi equations JO - Journal of Nonlinear Sciences and Applications SP - 6210--6227 VL - 9 IS - 12 AB - 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 \(m \geq 3\). 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. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.009.12.26 DO - 10.22436/jnsa.009.12.26 ID - Alzahrani2016 ER - TY - JOUR TI - Numerical discretization of the first-order Hamilton-Jacobi equation on triangular meshes AU - R. Abgrall JO - Comm. Pure Appl. Math. PY - 1996 DA - 1996// VL - 49 ID - Abgrall1996 ER - TY - JOUR TI - A parameterized multi-step Newton method for solving systems of nonlinear equations AU - F. Ahmad AU - E. Tohidi AU - J. A. Carrasco JO - Numer. Algorithms PY - 2016 DA - 2016// VL - 71 ID - Ahmad2016 ER - TY - JOUR TI - Higher order multi-step Jarratt-like method for solving systems of nonlinear equations: application to PDEs and ODEs AU - F. Ahmad AU - E. 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