Stability of the Radau IA and Lobatto IIIC methods for neutral delay differential system (Q5953933)

The authors study numerical stability of the linear neutral delay differential equations of the form NEWLINE\[NEWLINEu'(t)= Lu(t)+ Mu(t- \tau)+ Nu'(t- \tau),\quad t\geq 0,NEWLINE\]NEWLINE where \(L\), \(M\) and \(N\) are \(d\times d\) complex matrices. It has been shown that the Radau IA and Lobatto IIC methods equipped with suitable continuous extensions are NP-stable for the sealer case of the above system. In this paper the authors show that these methods have a similar stability property for the above system with complex matrices \(L\), \(M\) and \(N\). This property is also valid for arbitrary step size.