A very high-order finite volume method for the time-dependent convection–diffusion problem with Butcher Tableau extension

摘要: The time discretization of a very high-order nite volume method may give rise to new numerical diculties resulting into accuracy degradations. Indeed, for the simple onedimensional unstationary convection-diusi on equation instance, conicting situation between source term and boundary conditions arise when using standard Runge-Kutta method. We propose an alternative procedure by extending Butcher Tableau overcome this specic diculty achieve fourth-, sixth- or eighth-order schemes in space time. To end, is designed based polynomial reconstructions discretization, while we use Extended perform discretization. A large set tests has been carried out validate proposed