## AL-KHALED, K.:A Sinc-Galerkin approach on the *p*-system

### Saitama Mathematical Journal 1998(Vol. 16) pp.1-13

### Abstract

A Sinc-Galerkin procedure is developed for systems of conservation laws
of mixed hyperbolic-elliptic type.
Sinc approximations to both derivative and the indefinite integral reduce
the system to an explicit system of algebraic equations.
It is shown that Sinc-Galerkin approximations produce an error of order
*O*(exp(-*c*/*h*)).
The scheme is numerically tested on the van der Waals equation in fluid
dynamics.
We observe convergence with good resolution to the solution for various
Riemann problems.