Abstract
This paper introduces a characteristic method for solving linear first-order hyperbolic partial differential equations in two space dimensions. The algorithm employs rational Wachspress-type basis functions applied to a hexagonal discretization of the domain, integrated within the Eulerian-Lagrangian Localized Adjoint Method (ELLAM) framework. The proposed scheme preserves the strengths of characteristic methods and delivers accurate numerical results, even with large time steps. Computational tests conducted on standard benchmark problems illustrate the effectiveness of the method.