Stability of difference schemes for a class of partial differential equations (Q797267)

Difference methods are considered for the equation \(\partial u/\partial t=\alpha u^ q(\partial u/\partial x)+a(\partial^ pu/\partial x^ p)\) with integers \(p\geq 2\), \(q\geq 0\). For \(\alpha =0\) stability conditions are studied for twelve standard schemes by estimating the amplification factors. In addition, linearized stability of the Kruskal-Zabusky scheme is discussed for \(\alpha =a=1\).