Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902693 | Applied Numerical Mathematics | 2018 | 30 Pages |
Abstract
Approximate solutions of linear and nonlinear integral equations using methods related to an interpolatory projection involve many integrals which need to be evaluated using a numerical quadrature formula. In this paper, we consider discrete versions of the modified projection method and of the iterated modified projection method for solution of a Urysohn integral equation with a smooth kernel. For râ¥1, a space of piecewise polynomials of degree â¤râ1 with respect to an uniform partition is chosen to be the approximating space and the projection is chosen to be the interpolatory projection at r Gauss points. The orders of convergence which we obtain for these discrete versions indicate the choice of numerical quadrature which preserves the orders of convergence. Numerical results are given for a specific example.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Rekha P. Kulkarni, Gobinda Rakshit,