Instability in a class of explicit two‐time‐level semi‐Lagrangian schemes

Recently Gospodinov and collaborators derived a family of second‐order two‐time‐level semi‐Lagrangian schemes that contain an undetermined parameter α. It is shown that, when using one of these schemes to approximate the forcing terms in partial differential equations in a semi‐Lagrangian coordinate frame, the choice of α has a critical influence on the absolute stability of the method. Optimal stability properties are obtained by choosing α = ¼ which corresponds to the SETTLS scheme proposed by Hortal.