Stepsize Conditions for General Monotonicity in Numerical Initial Value Problems

M. N. Spijker
2007 SIAM Journal on Numerical Analysis  
For Runge-Kutta methods and linear multistep methods, much attention has been paid, in the literature, to special nonlinear stability properties indicated by the terms total-variationdiminishing (TVD), strong-stability-preserving (SSP), and monotonicity. Stepsize conditions, guaranteeing these properties, were studied, e.g., by Shu and Osher [J. In the present paper, we obtain a special stepsize condition guaranteeing the above properties, for a generic numerical process. This condition is best
more » ... s condition is best possible in a well defined and natural sense. It is applicable to the important class of general linear methods, and it can also be used to answer some open questions, for methods of which the above stability properties were studied earlier.
doi:10.1137/060661739 fatcat:z3nlfozsfraspijr3mq2q2dy3u