We investigate solution properties of a class of evolutionary partial differential equations
(PDEs) with viscous and inviscid regularization. An equation in this class of PDEs can be
written as an evolution equation, involving only first-order spatial derivatives, coupled with
the Helmholtz equation. A recently developed two-step iterative method (PH Chiu, L. Lee,
TWH Sheu, A dispersion-relation-preserving algorithm for a nonlinear shallow-water wave
equation, J. Comput. Phys. 228 (2009) 8034–8052) is employed to study this class of PDEs …

We investigate solution properties of a class of evolutionary partial differential equations
(PDEs) with viscous and inviscid regularization. An equation in this class of PDEs can be
written as an evolution equation, involving only first-order spatial derivatives, coupled with
the Helmholtz equation. A recently developed two-step iterative method (Chiu et al., JCP,
228,(2009), pp. 8034-8052) is employed to study this class of PDEs. The method is in
principle superior for PDE's in this class as it preserves their physical dispersive features. In …