A shooting method for singular nonlinear second order Volterra integro-differential equations.

Shaw, R.E.; Garey, L.E.

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On convergence of quadrature-differences method for linear singular integro-differential equations on the interval

A. I. Fedotov (2001)

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Here we propose and justify the quadrature-differences method for the full linear singular integro-differential equations with Cauchy kernel on the interval $(- 1, 1)$ . We consider equations of zero, positive and negative indices. It is shown, that the method converges to exact solution and the error estimate depends on the sharpness of derivative approximation and the smoothness of the coefficients and the right-hand side of the equation.