Numerical integration of positive linear differential-algebraic systems (Q1955638)

This paper develops numerical techniques for preserving the positivity as well as the algebraic constraints of linear positive differential algebraic equations. The key approach is the decomposition of \(Ex'= Ax+ f\) into its differential and algebraic components. It is shown that when applied to index one systems stiffly accurate Runge-Kutta methods preserve this positivity, but for higher index problems standard approaches are not suitable.