Stability analysis of extended block boundary value methods for linear neutral delay integro-differential equations

This paper is concerned with the stability of extended block boundary value methods B2VMs for the linear neutral delay integro-differential-algebraic equations NDIDAEs and the linear neutral delay integro-differential equations NDIDEs. It is proved that every A-stable B2VM can preserve the asymptotic stability of the exact solution of NDIDAEs under some certain conditions. A necessary and sufficient condition of the B2VMs to be asymptotically stable for NDIDEs is also obtained. A few numerical experiments confirm the expected results.