Numerical solution of Volterra–Fredholm integral equations using parameterized pseudospectral integration matrices

The main purpose of this work is to provide parameterized pseudospectral integration matrices (PPIMs) for solving Volterra–Fredholm integral equations. We present an exact, efficient, and stable approach for computing PPIMs. Furthermore, we provide a rigorous convergence analysis for the pseudospect...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 270; pp. 744 - 755
Main Author Tang, Xiaojun
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.11.2015
Subjects
Convergence analysis
Pseudospectral integration matrices
Volterra–Fredholm integral equations
Volterra–Fredholm integral equations
Pseudospectral integration matrices
Convergence analysis
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Summary:The main purpose of this work is to provide parameterized pseudospectral integration matrices (PPIMs) for solving Volterra–Fredholm integral equations. We present an exact, efficient, and stable approach for computing PPIMs. Furthermore, we provide a rigorous convergence analysis for the pseudospectral scheme with collocation at the Jacobi-type points in both L∞ and Lω(α,β)2 spaces. Numerical results confirm the spectral rate of convergence for the proposed pseudospectral schemes.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2015.08.076