Convergence of a first order scheme for a non-local eikonal equation

We prove the convergence of a first order finite difference scheme approximating a non-local eikonal Hamilton–Jacobi equation. The non-local character of the problem makes the scheme not monotone in general. However, by using in a convenient manner the convergence result for monotone scheme of Crandall–Lions, we obtain the same bound for the rate of convergence.