LAUSR

Abstract Construction of strong stability preserving second derivative diagonally implicit multistage integration methods (SDIMSIMs) as a subclass of second derivative general linear methods (SGLMs) with and without quadratic stability (QS) has been investigated. Examples of such methods with p = q = r = s = 2 , 3 and 4 have been constructed, where p is the order, q is the stage order, r is the number of external stages, and s is the number of internal stages of the method. To show the efficiency of the proposed methods together with verification of the order of convergence and capability of these methods in preserving some nonlinear stability properties such as total variation and positivity, several one dimensional numerical experiments are performed.