Analytical and computational methods for a class of nonlinear singular integral equations
| Autor: | Sonia Seyed Allaei, Magda Rebelo, Teresa Diogo |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Numerical Analysis
Applied Mathematics Uniform convergence Mathematical analysis 010103 numerical & computational mathematics Singular integral 01 natural sciences Integral equation Volterra integral equation Local convergence 010101 applied mathematics Computational Mathematics Nonlinear system symbols.namesake Singularity Singular solution symbols 0101 mathematics Mathematics |
| Zdroj: | Applied Numerical Mathematics. 114:2-17 |
| ISSN: | 0168-9274 |
| DOI: | 10.1016/j.apnum.2016.06.001 |
| Popis: | We consider a class of nonlinear singular Hammerstein Volterra integral equations. In general, these equations will have kernels containing both an end point and an Abel-type singularity, with exact solutions being typically nonsmooth. Under certain conditions, a uniformly convergent iterative solution is obtained on a small interval near the origin. In this work, two product integration methods are proposed and analyzed where the integral over a small initial interval is calculated analytically, allowing the optimal convergence rates to be achieved. This is illustrated by some numerical examples. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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