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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Veröffentlicht in:	Journal of scientific computing 2019-06, Vol.79 (3), p.1801-1813
Hauptverfasser:	Wei, Yunxia, Chen, Yanping
Format:	Artikel
Sprache:	eng
Schlagworte:	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
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Zusammenfassung:	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.
ISSN:	0885-7474 1573-7691
DOI:	10.1007/s10915-019-00912-7