FRACTIONAL HERMITE DEGENERATE KERNEL METHOD FOR LINEAR FREDHOLM INTEGRAL EQUATIONS INVOLVING ENDPOINT WEAK SINGULARITIES

Jiawei Guo; Tongke Wang

doi:10.11948/20190288

2020 Volume 10 Issue 5

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Jiawei Guo, Tongke Wang. FRACTIONAL HERMITE DEGENERATE KERNEL METHOD FOR LINEAR FREDHOLM INTEGRAL EQUATIONS INVOLVING ENDPOINT WEAK SINGULARITIES[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 1918-1936. doi: 10.11948/20190288

Citation:

Jiawei Guo, Tongke Wang. FRACTIONAL HERMITE DEGENERATE KERNEL METHOD FOR LINEAR FREDHOLM INTEGRAL EQUATIONS INVOLVING ENDPOINT WEAK SINGULARITIES[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 1918-1936. doi: 10.11948/20190288

FRACTIONAL HERMITE DEGENERATE KERNEL METHOD FOR LINEAR FREDHOLM INTEGRAL EQUATIONS INVOLVING ENDPOINT WEAK SINGULARITIES

Jiawei Guo^1, ,,
Tongke Wang^1, ,

1.
School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China

Corresponding authors: Email address: jiawei94@sina.cn(J. Guo); Email address: wangtke@sina.com(T. Wang)
Fund Project: This project is supported by the National Natural Science Foundation of China(grant No.11971241), the program for Innovative Research Team in Universities of Tianjin (TD13-5078) and 2017-Outstanding Young Innovation Team Cultivation Program of Tianjin Normal University (135202TD1703)

Abstract

Abstract

In this article, the Fredholm integral equation of the second kind with endpoint weakly singular kernel is considered and suppose that the kernel possesses fractional Taylor's expansions about the endpoints of the interval. For this type kernel, the fractional order interpolation is adopted in a small interval involving the singularity and piecewise cubic Hermite interpolation is used in the remaining part of the interval, which leads to a kind of fractional degenerate kernel method. We discuss the condition that the method can converge and give the convergence order. Furthermore, we design an adaptive mesh adjusting algorithm to improve the computational accuracy of the degenerate kernel method. Numerical examples confirm that the fractional order hybrid interpolation method has good computational results for the kernels involving endpoint weak singularities.
MSC: 45B05, 65R20

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References

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