Numerical Solution of Eikonal Equation Using Finite Difference Method

  • Sana'a Abdullah Alotibi Mrs.
Keywords: Wave Propagation, Eikonal Equation, Wave Front, Partial Differential Equation, Analytical Solutions, Tsunami Wave.

Abstract

In this paper, a method to calculate tsunami wave front is introduced using the finite difference method to solve the ill-posed problem and to calculate perturbed velocity of the wave front. Comparison between the actual and approximate solution will be proposed in a table form and a graphic form.

Author Biography

Sana'a Abdullah Alotibi, Mrs.

Department Mathematics, King Abdulaziz University, Rabigh, Kingdom of Saudi Arabia

References

Hitoshi Ishii, A Simple, Direct Proof of Uniqueness for So-lutions of the Hamilton-Jacobi Equations of Eikonal Type,1987.

E.D.Moskalensky, Finding exact solution to the Two-Dimensional eikonal equation, numerical analysis and applications,2009.

Marchuk, An.G., Chubarov, L.B., and Shokin, Yu.I., Chislennoe modelirovanie voln tsunami (Numerical Simulation of Tsunami Waves), Novosibirsk: Nauka, 1983.

An.G. Marchuk, E.D. Moskalensky, Some analytical solutions for tsunami wave rays and front,2010.

J.W.Thomas,Numerical Partial differential equation, spring science +business,inc,new York,1995.

Published
2018-12-31
How to Cite
Alotibi, S. (2018). Numerical Solution of Eikonal Equation Using Finite Difference Method. JOURNAL OF ADVANCES IN MATHEMATICS, 15, 8174-8184. https://doi.org/10.24297/jam.v15i0.7981
Section
Articles