Boundary treatment of linear multistep methods for hyperbolic conservation laws

When using high-order schemes to solve hyperbolic conservation laws in bounded domains, it is necessary properly treat boundary conditions so that the overall accuracy and stability are maintained. In [1, 2] a finite difference treatment method proposed for Runge-Kutta methods of laws. The combines an inverse Lax-Wendroff procedure WENO type extrapolation achieve desired stability. this paper, we further develop linear multistep (LMMs) We test through both 1D 2D benchmark numerical examples two third-order LMMs, one with constant time step other variable step. Numerical show expected high order excellent addition, approach [3] may be adopted deal exceptional case where eigenvalues flux Jacobian matrix change signs at boundary. These results demonstrate combined works very well LMMs