UNIFORM ASYMPTOTIC STABILITY OF STRANG'S EXPLICIT COMPACT SCHEMES FOR LINEAR ADVECTION

摘要

We consider a family of explicit compact schemes for advection in one dimension. The order is arbitrarily high. These stencils may be called Strang's stencils after the seminal work of Strang [J. Math. Phys., 41 (1962), pp. 147-154]. We prove that odd order schemes are stable in all L-q under CFL one. The strategy of the proof is similar to the one of Thomee [J. Differential Equations, 1 (1965), pp. 273-292] with a careful verification that all sharp estimates on the amplification factor are independent of the CFL number. This is possible based on a general representation formula for the amplification factor. Numerical results in one dimension confirm the analysis.