Abstract
Some Runge-Kutta methods for the numerical solution of Volterra integral equations of the second kind have been considered previously, and these methods can be generalized in a natural way. By considering a class of variable-step quadrature methods, the Runge-Kutta methods appear as extensions of the step-by-step quadrature methods, and theoretical insight is readily obtained. Such insight may provide confidence limits when constructing practical algorithms.
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7. References
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Baker, C.T.H. (1978). Runge-Kutta methods for Volterra integral equations of the second kind. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067691
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DOI: https://doi.org/10.1007/BFb0067691
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