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Wei, Yunxia; Chen, Yanping; Shi, Xiulian; Zhang, Yuanyuan

Spectral method for multidimensional Volterra integral equation with regular kernel. (English) Zbl 1416.65559

Front. Math. China 14, No. 2, 435-448 (2019).
Summary: This paper is concerned with obtaining an approximate solution for a linear multidimensional Volterra integral equation with a regular kernel. We choose the Gauss points associated with the multidimensional Jacobi weight function \(\omega(\boldsymbol x) = \prod{_{i=1}^d}(1 - x_i)^\alpha(1 + x_i)^\beta\), \(-1 <\alpha,\beta < \frac{1}{d} - \frac{1}{2}\) (\(d\) denotes the space dimensions) as the collocation points. We demonstrate that the errors of approximate solution decay exponentially. Numerical results are presented to demonstrate the effectiveness of the Jacobi spectral collocation method.

Cited in 6 Documents

MSC:

65R20 Numerical methods for integral equations
45D05 Volterra integral equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs

Keywords:

multidimensional Volterra integral equation; Jacobi collocation discretization; multidimensional Gauss quadrature formula
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References:

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