Open AccessA new Euler matrix method for solving systems of linear Volterra integral equations with variable coefficients
Author(s) -
Farshid Mirzaee,
Saeed Bimesl
Publication year - 2014
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2013.06.016
Subject(s) - mathematics , variable (mathematics) , volterra integral equation , coefficient matrix , collocation (remote sensing) , backward euler method , collocation method , matrix (chemical analysis) , euler's formula , euler method , mathematical analysis , system of linear equations , integral equation , euler equations , differential equation , computer science , ordinary differential equation , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , machine learning , composite material
This article develops an efficient solver based on collocation points for solving numerically a system of linear Volterra integral equations (VIEs) with variable coefficients. By using the Euler polynomials and the collocation points, this method transforms the system of linear VIEs into the matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Euler coefficients. A small number of Euler polynomials is needed to obtain a satisfactory result. Numerical results with comparisons are given to confirm the reliability of the proposed method for solving VIEs with variable coefficients