Strong stability preserving second derivative multistep methods

This paper focuses on the analysis and development of strong stability properties for the second derivative multistep methods (SDMMs). By obtaining the strong stability preserving (SSP) conditions for this class of methods, we present SSP SDMMs in general and Adams-type forms. These novel methods exhibit larger SSP coefficients compared to the existing SSP linear multistep methods. To validate the theoretical claims and assess the performance of the proposed methods, some numerical experiments are performed on the both scalar and systems of equations conforming the expected theoretical behavior in terms of the convergence order.