Superconvergence in the maximum norm of a class of piecewise polynomial collocation methods for solving linear weakly singular Volterra integro-differential equations (Q1885582)

The authors use a piecewise polynomial collocation method on graded grids for solving linear weakly singular integro-differential equations of the Volterra type. It is proved that a careful choice of the collocation parameters improves the convergence rate of the method. Moreover, the error estimates for all values of the nonuniformity parameter of the grid are obtained.