General formulation of second-order semi-Lagrangian methods for convection-diffusion problems
Summary: The general formulation of the second-order semi-Lagrangian methods is presented for convection-dominated diffusion problems. In view of the method of lines, this formulation is in a sufficiently general fashion as to include the two-step backward difference formula and Crank-Nicolson type semi-Lagrangian schemes as particular ones. It is easy to be extended to higher-order schemes. We show that it maintains second-order accuracy even if the involved numerical characteristic lines are first-order accurate. The relationship between semi-Lagrangian methods and the modified method of characteristic is also addressed. Finally, convergence properties of the semi-Lagrangian finite difference schemes are tested.
scientific article; zbMATH DE number 6161371
scientific article