The p-stability and q-stability of singly diagonally implicit runge-kutta method for delay differential equations - Ismail, Fudziah; Suleiman, Mohamed (Gordon & Breach Science Publ IncNewark, 2000)
The stability properties for Singly Diagonally Implicit Runge-Kutta method fourth order five stages embedded in fifth order six stages, combined with Lagrange interpolation when applied to the linear delay differential equation. y′(t) = λy(t)+μy(t-τ) (t≥0), y(t) = φ(t) (t∈[-τ, 0]) are investigated. Their regions of stability for (λ, μ∈R) and (μ∈C, λ = 0) are determined and numerical results when some problems are solved using the method are presented.