A kernel-based method for parabolic equations with nonlinear convection terms

Abstract

We present an algorithm for parabolic equations with (possibly nonlinear) convective terms, based on our earlier work using linear semigroup methods. Here the semigroup is used to decouple the convective term to allow for a two-stage solution process. The method is shown to be asymptotically stable and second-order accurate, with the stability being independent of the mesh parameters and the convective term.