Abstract: An initial-boundary value problem for a system of nonlinear partial differential equations which consists of a hyperbolic and a parabolic part is taken into consideration. Spacial derivatives are discretised by third order consistent difference operators which are constructed such that a summation--by--parts formula holds. Therefore, the space discretisation is energy bounded and algebraically stable implicit Runge-Kutta methods can be applied to integrate in time. Boundary layers arising from the artificial boundary conditions are analysed and nonlinear convergence is proved.
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