Higher-order finite difference schemes for the magnetic induction equations with resistivity

In this paper we design high-order accurate and stable finite difference schemes for the initial-boundary-value problem associated with the magnetic induction equation with resistivity. We use summation-by-parts finite difference operators to approximate spatial derivatives and a simultaneous approximation term technique for implementing boundary conditions. The resulting schemes are shown to be energy stable. Various numerical experiments demonstrating both the stability and the high order of accuracy of the schemes are presented.