The use of a Legendre pseudospectral viscosity technique to solve a class of nonlinear dynamic Hamilton–Jacobi equations

In this research, we study the problem of finding the approximate solution of a class of Hamilton–Jacobi equations, namely the Eikonal equation. We employ the Legendre pseudospectral viscosity method to solve this problem. This method basically consists of adding a spectral viscosity to the equation. This spectral viscosity, which is sufficiently small to retain the formal spectral accuracy is large enough to stabilize the numerical scheme. Several test problems are considered and the numerical results are given to show the efficiency of the proposed method.