Numerical solution of a nonlinear singular Volterra integral system by the Newton product integration method

In this paper, we consider a nonlinear system of Volterra integral equations, and apply Newton’s method to linearize it. We solve each step of Newton’s system by the product integration technique. Also, we provide the sufficient conditions for convergence of the numerical method. Finally, we give a...

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Bibliographic Details
Published inMathematical and computer modelling Vol. 58; no. 11-12; pp. 1696 - 1703
Main Authors Babayar-Razlighi, B., Soltanalizadeh, B.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.12.2013
Subjects
equations
Newton’s method
Numerical solution
Product integration technique
product system
System of Volterra integral equations
Weakly singular
Weakly singular
Newton’s method
System of Volterra integral equations
Product integration technique
Numerical solution
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Summary:In this paper, we consider a nonlinear system of Volterra integral equations, and apply Newton’s method to linearize it. We solve each step of Newton’s system by the product integration technique. Also, we provide the sufficient conditions for convergence of the numerical method. Finally, we give a test problem to illustrate the applicability and accuracy of the presented method.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2013.06.016