Numerical comparison of methods for solving systems of conservation laws of mixed type

In this paper, we apply Adomian decomposition method (shortly, ADM) to develop a fast and accurate algorithm for systems of conservation laws of mixed hyperbolic-elliptic type. The ADM does not require discretization and consequently of massive computations. A Sinc-Galerkin procedure is also developed for solving the same system. Sinc approximations to both derivatives and the indefinite integrals reduce the system to an explicit system of algebraic equations. It is shown that Sinc-Galerkin approximations produce an error of exponential order. Approximation by Sinc functions handles singularities in the problem, as well as changes in type of the system. A comparison between the two methods for the solution of Van der Waals system is analyzed for their solutions. The study outlines the significant features of the two methods. The results show that these methods are very efficient, convenient and can be applied to a large class of problems.