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Fast Runge-Kutta methods for nonlinear convolution systems of Volterra integral equations. (English) Zbl 1116.65128
Summary: In this paper fast implicit and explicit Runge-Kutta methods for systems of Volterra integral equations of Hammerstein type are constructed. The coefficients of the methods are expressed in terms of the values of the Laplace transform of the kernel. These methods have been suitably constructed in order to be implemented in an efficient way, thus leading to a very low computational cost both in time and in space. The order of convergence of the constructed methods is studied. The numerical experiments confirm the expected accuracy and computational cost. I suggest to compare this technique with Adomian decomposition method very suitable for integral equations.

MSC:
65R20 Numerical methods for integral equations
45D05 Volterra integral equations
44A35 Convolution as an integral transform
44A10 Laplace transform
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