Order-optimal methods for integro-differential equations in the singular case
type: Item
instance of: scholarly article
title: Order-optimal methods for integro-differential equations in the singular case
zbMATH Open document ID: 1359.65306
DOI: 10.1134/S0012266116090123
published in: Differential Equations
publication date: 2017-02-07T00:00:00Z
review text: The paper is concerned with a linear integro-differential equation of the third kind with a coefficient which has zeros of finite orders. The aim of the paper is to consider a new type of spline approximation based on generalised functions derived from the Dirac delta function. The author considers a generalised polygonal method and a generalised parabolic spline subdomain method, provides an error estimate for approximate solutions, and explores the optimisation of direct projection methods for third kind equations.
reviewed by: Neville J. Ford
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45A05
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 6681162
zbMATH Keywords: integro-differential equation
zbMATH Keywords: spline methods
zbMATH Keywords: generalised functions
zbMATH Keywords: generalised polygonal method
zbMATH Keywords: parabolic spline subdomain method
zbMATH Keywords: error estimate
author: N. S. Gabbasov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6681162