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In the present paper we consider discrete versions of the modified projectionmethods for solving a Urysohn integral equation with a kernel of the type ofGreen's function. For $r \geq 0,$ a space of piecewise polynomials of degree$\leq r $ with respect to an uniform partition is chosen to be theapproximating space. We define a discrete orthogonal projection onto this spaceand replace the Urysohn integral operator by a Nystr\"{o}m approximation. Theorder of convergence which we obtain for the discrete version indicates thechoice of numerical quadrature which preserves the orders of convergence in thecontinuous modified projection methods. Numerical results are given for aspecific example.

Discrete Modified Projection Methods for Urysohn Integral Equations with Green's Function Type Kernels