Special versions of the collocation method for integro-differential equations in the singular case
type: Item
instance of: scholarly article
title: Special versions of the collocation method for integro-differential equations in the singular case
zbMATH Open document ID: 1380.65437
DOI: 10.1134/S0012266117090117
published in: Differential Equations
publication date: 2017-12-18T00:00:00Z
review text: The paper discusses two numerical methods for solving the linear singular Fredholm integro-differential equation \(x(t) \prod_{j=1}^q (t - t_j)^{m_j} + \sum_{j=0}^p \int_{-1}^1 K_j(t,s) x^{(j)}(s) ds = y(t)\). The methods are of collocation type. The first method is based on Bernstein operators, the second one employs Hermite-Fejér interpolation techniques. An error analysis is provided in both cases.
reviewed by: Kai Diethelm
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45A05
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 6819864
zbMATH Keywords: collocation method
zbMATH Keywords: Bernstein polynomial
zbMATH Keywords: Hermite-Fejér interpolation
zbMATH Keywords: error bound
zbMATH Keywords: linear singular Fredholm integro-differential equation
author: N. S. Gabbasov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6819864