A first-order hyperbolic system approach for dispersion

- We propose a new first-order hyperbolic system approach for dispersive partial differential equations.
- We apply a compact 4th-order RD scheme, and solve time dependent dispersive PDEs.
- We demonstrate the performance of the high-order RD schemes on the proposed hyperbolic system, including dispersive shock cases.
- We verify that the predicted solution, its gradient and Hessian have the same order of accuracy on randomly distributed nodes.