document: Stability of Runge-Kutta methods for delay integro-differential equations We study stability of Runge-Kutta -LRB- RK -RRB- methods for delay integro-differential equations with a constant delay on the basis of the linear equation du/dt = Lu -LRB- t -RRB- + Mu -LRB- t - tau -RRB- + K integral / sub t - tau / / sup t / u -LRB- theta -RRB- d theta , where L , M , K are constant complex matrices . In particular , we show that the same result as in the case K = 0 -LRB- Koto , 1994 -RRB- holds for this test equation , i.e. , every A-stable RK method preserves the delay-independent stability of the exact solution whenever a step-size of the form h = tau / m is used , where m is a positive integer
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