Numerical solution of Volterra integral equations with singularities

Abstract

The numerical solution of linear Volterra integral equations of the second kind is discussed. The kernel of the integral equation may have weak diagonal and boundary singularities. Using suitable smoothing techniques and polynomial splines on mildly graded or uniform grids, the convergence behavior of the proposed algorithms is studied and a collection of numerical results is given.

Key words： Boundary singularity; collocation method; smoothing transformation; Volterra integral equation; weakly singular kernel

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