Exact optimal values of step-size coefficients for boundedness of linear multistep methods (Q1744041)

Initial value problems of ordinary differential equations are discretized with linear multistep methods and their monotonicity and boundedness properties are analyzed. Three families of multistep methods are studied, extrapolated backwards differencing schemes (BDF), implicit BDF methods, and Adam-Bashforth methods, which are explicit. Step-size coefficients for monotonicity are derived, which are a generalization of the strong-stability-preserving coefficients. Methods to check rigorously the sign conditions on linear recursions associated to the different numerical methods are proposed and optimal values of the step-size coefficients are explicitly computed.