Explicit Runge-Kutta Methods for the Numerical Solution of Singular Delay Differential Equations
Christopher T.H. Baker & Christopher A.H. Paul
Explicit Runge-Kutta, singular delay differential equations
Report No.
27th April 1992
Revised version published in Advances in Computational Mathematics
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In this paper, we are concerned with the deverlopment of an explicit Runge-Kutta scheme for the numerical solution of delay differential equations (DDEs) where one or more delay lies in the current Runge-Kutta interval. The scheme presented is also applicable to the numerical solution of Volterra functional equations (VFEs), although the theory is not covered in this paper. We also derive the stability equations of the scheme for the ODE
y'(t) = l y(t),
and the DDE
y'(t) = l y(t) + u y(t-T),

where the delay T and the Runge-Kutta stepsize H are both constant. In the case of the DDE, we consider the two distinct cases: (i) T >= H, and (ii) T < H. We evaluate the performance of the scheme by solving several types of singular DDE and VFE.
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