An efficient asymptotic-numerical method to solve nonlinear systems of one-dimensional balance laws

An asymptotic-numerical method to solve the initial-boundary value problems for systems of balance laws in one space dimension, on the half space is developed. Expansions in powers of t -1/ 2 are used, in view of the precise asymptotic behavior recently established on theoretical bases. This approach increases considerably the efficiency of a previous one, where just expansions in inverse powers of t were made. Numerical examples and comparisons with the Godunov, the asymptotic high order, and the asymptotic-numerical method earlier developed are presented. Expanding the solution in powers of t -1/ 2 instead of t -1, a saving of about one-half of the CPU time can be realized, still achieving the same accuracy.