Regularizing properties of difference schemes for singular integral-differential equations
type: Item
instance of: scholarly article
title: Regularizing properties of difference schemes for singular integral-differential equations
zbMATH Open document ID: 1256.65105
published in: Applied Numerical Mathematics
publication date: 2012-09-26T00:00:00Z
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G05
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 6086861
zbMATH Keywords: system of singular integral-differential equations
zbMATH Keywords: Adams quadrature formulas
zbMATH Keywords: stability
zbMATH Keywords: difference schemes
author: E. V. Chistyakova
reviewed by: Ivan Secrieru
MaRDI profile type: Publication
full work available at URL: j.apnum.2012.06.006
OpenAlex ID: W1967948674
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DOI: 10.1016/J.APNUM.2012.06.006
review text: The author studies in the space \( C^{'}[0,1] \) a system of integral-differential equations of the form NEWLINE\[NEWLINE A(t) x'(t) + B(t) x(t) = F( t,\int^{t}_{0}K(t,s,x(s))ds),\qquad t\in [0,1], NEWLINE\]NEWLINE with the initial condition \( x(0)= x_{0}\). It is assumed that the matrix \(A(t)\) satisfies the condition NEWLINE\[NEWLINE det A= 0,\qquad \forall t\in [0,1].NEWLINE\]NEWLINE The approximate system for this problem is constructed using the backward differentiation formula of order \(k\) for the derivative \( x'(t)\) and the Adams quadrature formula to approximate the integral with the variable upper limit. The author proves that this difference scheme can be stable using the step size \(h\) as a regularization parameter.
description: scientific article; zbMATH DE number 6086861