2024 : 11 : 9
Mohammad Reza Azimi

Mohammad Reza Azimi

Academic rank: Associate Professor
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Education: PhD.
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Faculty: 1
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Research

Title
Numerical solution of a class of nonlinear Volterra integral equations using Bernoulli operational matrix of integration
Type
JournalPaper
Keywords
nonlinear integral equations, Volterra integral equations, Bernoulli polynomials, operational matrix, collocation method
Year
2015
Journal Acta Universitatis Matthiae Belii, series Mathematics
DOI
Researchers Sohrab Bazm ، Mohammad Reza Azimi

Abstract

In this paper, a simple efficient method for the numerical solution of a class of nonlinear Volterra integral equations (VIEs) is presented. The approach starts by expanding the existing functions in terms of Bernoulli polynomials. Subsequently, using the new introduced Bernoulli operational matrices of integration and the product along with the so-called collocation method, the considered problem is reduced into a set of nonlinear algebraic equations with unknown Bernoulli coefficients. The error analysis and rate of convergence are also given. Finally, some tests of other authors are included and a comparison has been done between the results.