Open AccessConvergence analysis of the generalized Euler-Maclaurin quadrature rule for solving weakly singular integral equations
Author(s) -
Grzegorz Rządkowski,
Emran Tohidi
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1906801r
Subject(s) - mathematics , convergence (economics) , quadrature (astronomy) , mathematical analysis , integral equation , singular integral , nyström method , volterra integral equation , economic growth , electrical engineering , economics , engineering
In the present paper we use the generalized Euler-Maclaurin summation formula to study the convergence and to solve weakly singular Fredholm and Volterra integral equations. Since these equations have different nature, the proposed convergence analysis for each equation has a different structure. Moreover, as an application of this summation formula, we consider the numerical solution of the fractional ordinary differential equations (FODEs) by transforming FODEs into the associated weakly singular Volterra integral equations of the first kind. Some numerical illustrations are designed to depict the accuracy and versatility of the idea.