Discrete Modified Projection Method for Urysohn Integral Equations with Smooth Kernels
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 iter...
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| Format | Journal Article |
| Language | English |
| Published |
02.08.2017
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| 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 methodfor solution of a Urysohn integral equation
with a smooth kernel. For $r \geq 1,$ a space of piecewise polynomials of
degree less than or equal to r - 1 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. |
|---|---|
| AbstractList | 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 methodfor solution of a Urysohn integral equation
with a smooth kernel. For $r \geq 1,$ a space of piecewise polynomials of
degree less than or equal to r - 1 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. |
| Author | Kulkarni, Rekha P Rakshit, Gobinda |
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| BackLink | https://doi.org/10.48550/arXiv.1708.00599$$DView paper in arXiv |
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| Snippet | Approximate solutions of linear and nonlinear integral equations using
methods related to an interpolatory projection involve many integrals which
need to be... |
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| SubjectTerms | Mathematics - Numerical Analysis |
| Title | Discrete Modified Projection Method for Urysohn Integral Equations with Smooth Kernels |
| URI | https://arxiv.org/abs/1708.00599 |
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