The use of variational iteration method and Adomian decomposition method to solve the Eikonal equation and its application in the reconstruction problem

摘要

In this paper, the variational iteration method (VIM) and the Adomian decomposition method (ADM) are applied to solve the Eikonal equation. In addition, we apply the VIM using He's polynomials to find a semi-analytic solution of the studied model. The VIM is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. On the other hand, in the ADM the approximate solution is considered as an infinite series usually converging to the accurate solution. In addition, the results obtained using the two methods are presented. Comparison of the results reveals that the present methods are very efficient and convenient.