A truly noninterpolating semi-Lagrangian Lax-Wendroff method (Q1331431)

This paper deals with the development of numerical methods for the solution of a class of advection-diffusion equations in which the term of the advective velocity is the dominant term in the differential equation. The schemes proposed here are semi-Lagrangian and noninterpolant and are based upon the ideas which lead to the one step Lax-Wendroff algorithm. This implies that the new algorithm is explicit, second order accurate in both time and space and unconditionally stable for a rectangular regular grid. Moreover, being explicit and noninterpolatory, its computational cost turns out to be very small. Finally, some numerical experiments are presented to show that the new scheme is able to provide numerical results which are in agreement with the expected accuracy of the method.