Stability analysis of inverse Lax–Wendroff boundary treatment of high order compact difference schemes for parabolic equations

In this paper, we study the stability of a numerical boundary treatment high order compact finite difference methods for parabolic equations. The schemes could achieve very accuracy with relatively small stencils. To match convergence in interior domain, take simplified inverse Lax–Wendroff (SILW) procedure (Tan et al., 2012; Li 2017) as our treatment. third total variation diminishing (TVD) Runge–Kutta method (Shu and Osher, 1988) is taken time-stepping fully-discrete case. Two analysis techniques are adopted to check algorithm’s stability, one based on Godunov–Ryabenkii theory, other eigenvalue spectrum visualization (Vilar Shu, 2015). Both semi-discrete cases investigated, these two different yield consistent results. Several experimental results shown validate theoretical