A Jacobi Spectral Method for Solving Multidimensional Linear Volterra Integral Equation of the Second Kind

The subject of the present paper is to apply the Jacobi spectral collocation method for multidimensional linear Volterra integral equation with a weakly singular kernel. Here, we assume that the solution is sufficiently smooth. An error analysis has been provided which justifies that the approximate...

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Bibliographic Details
Published inJournal of scientific computing Vol. 79; no. 3; pp. 1801 - 1813
Main Authors Wei, Yunxia, Chen, Yanping
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2019
Springer Nature B.V
Subjects
Algorithms
Banach spaces
Collocation methods
Computational Mathematics and Numerical Analysis
Error analysis
Exact solutions
Hilbert space
Inequality
Integral equations
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical functions
Mathematics
Mathematics and Statistics
Partial differential equations
Spectral methods
Theoretical
Volterra integral equations
65N12
65R20
Multidimensional linear Volterra integral equation
45J05
Multidimensional Gauss quadrature formula
Jacobi collocation discretization
Convergence analysis
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Summary:The subject of the present paper is to apply the Jacobi spectral collocation method for multidimensional linear Volterra integral equation with a weakly singular kernel. Here, we assume that the solution is sufficiently smooth. An error analysis has been provided which justifies that the approximate solution converges exponentially to the exact solution. Finally, two numerical examples are given to clarify the efficiency and accuracy of the method.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-019-00912-7