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 计算数学  2019, Vol. 41 Issue (1): 66-81    DOI:
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FRACTIONAL ORDER DEGENERATE KERNEL METHODS FOR FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND WITH ENDPOINT SINGULARITIES
Wang Tongke, Fan Meng
School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China
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Abstract： This paper constructs fractional order degenerate kernel methods based on the fractional Taylor's expansion for Fredholm integral equations of the second kind with endpoint singularities. Two computational schemes are designed, one is approximating the kernel function by its fractional Taylor's expansion in the whole interval, and the other is constructing a fractional order interpolation in a small interval containing the singularity and using piecewise quadratic interpolation to approximate the kernel function in the remaining part of the interval. The conditions that the two degenerate kernel methods converge are discussed, and the convergence order is estimated for hybrid interpolation scheme. Numerical examples demonstrate that the fractional order degenerate kernel methods have good computational results for the kernel functions with endpoint singularities, and the hybrid quadratic interpolation scheme has broader scope of application than the fractional order degenerate kernel method in the whole interval.

 引用本文: . 第二类端点奇异Fredholm积分方程的分数阶退化核方法[J]. 计算数学, 2019, 41(1): 66-81. . FRACTIONAL ORDER DEGENERATE KERNEL METHODS FOR FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND WITH ENDPOINT SINGULARITIES[J]. Mathematica Numerica Sinica, 2019, 41(1): 66-81.

 [1] Sloan I H. Error analysis for a class of degenerate-kernel methods[J]. Numer. Math., 1976, 25(3):231-238. [2] Sloan I H. Convergence of degenerate kernel methods[J]. J. Aust. Math. Soc. Series B-Appl. Math., 1976, 19(4):422-431. [3] Atkinson K E. The Numerical Solution of Integral Equations of the Second Kind[M]. Cambridge University Press, 1997. [4] Karimi S, Jozi M. Numerical solution of the system of linear Fredholm integral equations based on degenerating kernels[J]. TWMS J. Pure Appl. Math., 2015, 6(1):111-119. [5] Hämmerlin G, Schumaker L L. Procedures for kernel approximation and solution of Fredholm integral equations of the second kind[J]. Numer. Math., 1980, 34:125-141. [6] Wazwaz A M. Linear and Nonlinear Integral Equations:Methods and Applications[M]. Berlin:Springer-Verlag, 2011. [7] Dellwo D R. Accelerated degenerate-kernel methods for linear integral equations[J]. J. Comput. Appl. Math., 1995, 58(2):135-149. [8] Guebbai H, Grammont L. A new degenerate kernel method for a weakly singular integral equation[J]. Appl. Math. Comput., 2014, 230:414-427. [9] 沈以淡. 积分方程(第3版)[M]. 北京:清华大学出版社, 2012. [10] Kaneko H, Xu Y S. Degenerate kernel method for Hammerstein equations[J]. Math. Comp., 1991, 56(193):141-148. [11] Ikebe Y. The Galerkin method for the numerical solution of Fredholm integral equations of the second kind[J]. SIAM Rev., 1972, 14(3):465-491. [12] Okayama T, Matsuo T, Sugihara M. Sinc-collocation methods for weakly singular Fredholm integral equations of the second kind[J]. J. Comput. Appl. Math., 2010, 234(4):1211-1227. [13] Atkinson K E, Shampine L F. Algorithm876:Solving Fredholm integral equations of the second kind in Matlab[J]. ACM Trans. Math. Software, 2008, 34(4), Article 21:1-20. [14] Occorsio D, Russo M G. Numerical methods for Fredholm integral equations on the square[J]. Appl. Math. Comput., 2011, 218(5):2318-2333. [15] Orav-Puurand K, Pedas A, Vainikko G. Nyström type methods for Fredholm integral equations with weak singularities[J]. J. Comput. Appl. Math., 2010, 234(9):2848-2858. [16] Giuseppe M, Gradimir V. M. Well-conditioned matrices for numerical treatment of Fredholm integral equations of the second kind[J]. Numer. Linear Algebra Appl., 2009, 16(11-12):995-1011. [17] Chen Q S, Lin F R. A modified Nyström-Clenshaw-Curtis quadrature for integral equations with piecewise smooth kernels[J]. Appl. Numer. Math., 2014, 85:77-89. [18] 王同科, 佘海艳, 刘志方. 分数阶光滑函数线性和二次插值公式余项估计[J]. 计算数学, 2014, 36(4):393-406. 浏览 [19] Kolwankar K M. Recursive local fractional derivative[J]. arXiv preprint arXiv:1312.7675(2013). [20] Liu Z F, Wang T K, Gao G H. A local fractional Taylor expansion and its computation for insufficiently smooth functions[J]. East Asian Journal on Applied Mathematics, 2015, 5(2):176-191. [21] Wang T K, Li N, Gao G H. The asymptotic expansion and extrapolation of trapezoidal rule for integrals with fractional order singularities[J]. Int. J. Comput. Math., 2015, 92(3):579-590. [22] Wang T K, Liu Z F, Zhang Z Y. The modified composite Gauss type rules for singular integrals using Puiseux expansions[J]. Math. Comp, 2017, 86(303):345-373. [23] Wang T K, Zhang Z Y, Liu Z F. The practical Gauss type rules for Hadamard finite-part integrals using Puiseux expansions[J]. Adv. Comput. Math., 2017, 43(2):319-350. [24] Wang T K, Gu Y S, Zhang Z Y. An algorithm for the inversion of Laplace transforms using Puiseux expansions[J]. Numer. Algorithms, 2018, 78(1):107-132. [25] 樊梦, 王同科, 常慧宾. 非光滑函数的分数阶插值公式[J]. 计算数学, 2016, 38(2):212-224. 浏览
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