[1]闫 洁,韩惠丽*,陆万顺,等.非线性分数阶Fredholm积分方程的B样条小波解法[J].江西师范大学学报(自然科学版),2020,(06):604-608.[doi:10.16357/j.cnki.issn1000-5862.2020.06.10]
　YAN Jie,HAN Huili*,LU Wanshun,et al.The Numerical Solution of Nonlinear Fractional-Order Fredholm Integral Equation by B-Spline Wavelet Collocation Method[J].Journal of Jiangxi Normal University:Natural Science Edition,2020,(06):604-608.[doi:10.16357/j.cnki.issn1000-5862.2020.06.10]
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非线性分数阶Fredholm积分方程的B样条小波解法()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2020年06期
页码:
604-608
栏目:
出版日期:
2020-12-20

文章信息/Info

Title:
The Numerical Solution of Nonlinear Fractional-Order Fredholm Integral Equation by B-Spline Wavelet Collocation Method
文章编号:
1000-5862(2020)06-0604-05
作者:
闫 洁1; 2; 韩惠丽2*; 陆万顺1; 马 旭1
1.宁夏师范学院数学与计算机科学学院,宁夏 固原 756000; 2.宁夏大学数学统计学院,宁夏 银川 750021
Author(s):
YAN Jie1; 2; HAN Huili2*; LU Wanshun1; MA Xu1
1.School of Mathematics and Computer Science,Ningxia Normal University,Guyuan Ningxia 756000,China; 2.School of Mathematics Statistics Science,Ningxia University,Yinchuan Ningxia 750021,China
关键词:
分数阶微积分;  B样条小波;  Fredholm积分方程;  配置法
Keywords:
fractional calculus;  B-spline wavelet;  Fredholm integral equation;  collocation
分类号:
O 175.5
DOI:
10.16357/j.cnki.issn1000-5862.2020.06.10
文献标志码:
A
摘要:
利用B样条小波函数数值求解非线性分数阶第2类Fredholm积分方程,将具有紧支集的线性半正交B样条尺度函数和小波函数一起应用于数值求解非线性分数阶第2类Fredholm积分方程中.这种方法将非线性分数阶Fredholm积分方程转化为非线性代数方程组,再通过数值求解方程组得到原方程的数值解, 证明了误差边界值,数值算例验证了本方法的有效性和准确性.
Abstract:
The semiorthogonal B-spline wavelet are used to solve the solution of fractional-order Fredholm integral equation of the second kind.Compactly supported linear semiorthogonal B-spline scaling functions and wavelet functions are applied to approximate the solutions of nonlinear fractional-order Fredholm integral equation of the second kind.This method reduces the nonlinear fractional-order Fredholm integral equation to a nonlinear system of algebraic equations,numerical solution of original equation is obtained through solving algebraic equations and error bound value is estimated.Finally,some examples demonstrate the validity and precision of this method.

参考文献/References:

[1] 杨福生.小波变换的工程分析与应用[M].北京:科学出版社,2001.
[2] 李晟.小波与频谱分析[D].上海:上海交通大学,2009.
[3] 徐振民.高维空间的框架多分辨分析与小波[D].青岛:山东科技大学,2007.
[4] 郑小洋.积分方程和微分方程的几种基于小波的新型数值解法[D].重庆:重庆大学,2011.
[5] Yüzbasi S,Sezer M,Kemanci B.Numerical solutions of integro-differential equations and application of a population model with an improved Legendre method[J].Applied Mathematical Modelling,2013,37(4):2086-2101.
[6] Parand K,Delafkar Z,Pakniat N,et al.Collocation method using sinc and rational Legendre functions for solving Volterra’s population model[J].Commun Nonlinear Sci Numer Simulat,2011,16(4):1811-1819.
[7] 朱琪.高次插值的龙格现象的测试[J].湖南科技学院学报,2005,26(11):206-208.
[8] Hetmaniok E,Nowak I,Slota D,et al.A study of the convergence of and error estimation for the homotopy perturbation method for the Volterra-Fredholm integral equations[J].Applied Mathematics Letters,2013,26(1):165-169.
[9] Sakar M G,Uludag F,Erdogan F.Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method[J].Applied Mathematical Modelling,2016,40(13/14):6639-6649.
[10] Chang S H.Convergence of variational iteration method applied to two-point diffusion problems[J].Applied Mathematical Modelling,2016,40(15/16):6805-6810.
[11] Wazwaz A M,Rach R,Duan J.The modified Adomian decomposition method and the noise terms phenomenon for solving nonlinear weakly-singular Volterra and Fredholm Integral equations[J].Cent Eur J Eng,2013,3(4):669-678.
[12] 全晓静.非线性分数阶积分方程的Adomian解法[D].银川:宁夏大学,2015.
[13] Sahu P K,Saha Ray S.Legendre wavelets operational method for the numerical solutions of nonlinear Volterra integro-differential equations system[J].Applied Mathematics and Computation,2015,256:715-723.
[14] Zhou Fengying,Xu Xiaoyong.The third kind chebyshev wavelets collocation method for solving the time-fractional convection diffusion equations with variable coefficients[J].Applied Mathematics and Computation,2016,280:11-29.
[15] Yi Mingxu,Huang Jun.CAS wavelet method for solving the fractional integro-differential equation with a weakly singular kernel[J].International Journal of Computer Mathematics,2015,92(8):1715-1728.
[16] 虎晓燕.分数阶积分微分方程的无网格重心插值配点法[D].银川:宁夏大学,2016.
[17] 刘明才.小波分析及其应用[M].北京:清华大学出版社,2013.
[18] 雷开彬,马志霞,黄天云.基于de Boor-Cox递推公式的样条函数[C]∥中国计算机图形学进展2006第六届中国计算机图形学术大会论文集.杭州:中国计算机学会,2006:29-33.
[19] Goswami J C,Chan A K,Chui C K.On solving first-kind integral equations using wavelets on a bounded interval[J].IEEE Trans,Antennas Propag,1995,43(6):614-622.
[20] 吴光旭.第2类非线性Fredholm积分方程的迭代Galerkin法[D].成都:电子科技大学,2012.

备注/Memo

备注/Memo:
收稿日期:2018-09-16
基金项目:国家自然科学基金(1126104111762016),宁夏高等学校科学研究课题(NGY2018-137),宁夏高等学校一流学科建设(教育学学科)(NXYLXK2017B11)和宁夏师范学院校级科研课题(NXSFZDC1803)资助项目.
通信作者:韩惠丽(1972-),女,河北正定人,教授,博士,主要从事复分析及其应用以及积分方程数值解法研究.E-mail:nxhan@126.com
更新日期/Last Update: 2020-12-20