基于B样条小波的积分算子
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摘要
由于B样条函数及其对应的小波不具有平移正交性,推导半正交B样条小波的分数阶积分算子矩阵,为分数阶微积分方程的数值求解提供了理论基础.
In this paper,fractional integral operator matrix of semi-orthogonal B spline Wavelet is inferred,because of the B spline basic function and its corresponding wavelets have no transformation orthogonality. The result provides theoretical basis for numerical solution of fractional calculus equation.
In this paper,fractional integral operator matrix of semi-orthogonal B spline Wavelet is inferred,because of the B spline basic function and its corresponding wavelets have no transformation orthogonality. The result provides theoretical basis for numerical solution of fractional calculus equation.
引文
[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]黄洁,韩惠丽.应用Lengendre小波求解非线性分数阶Volterra积分微分方程[J].吉林大学学报(理学版),2014,52(7):655-660.
[5]黄洁.非线性分数阶Volterra积分微分方程的小波数值解法[D].银川:宁夏大学,2015.
[6]白如越,韩惠丽.一类种群模型的第三类Chebyshev小波解法[J].宁夏大学学报(自然科学版),2018,39(1):32-37.
[7]罗世平.来自多尺度分析的Riesz基[J].华南师范大学学报(自然科学版),2006,50(3):7-11.
[8]雷开彬,马志霞,黄天云.基于Cox-de Boor递推公式的样条函数[C].中国计算机图形学大会,2006.
[9]Goswami J C,Chan A K,Chui C K.On Solving Firstkind Integral Equations Using Wavelets on a Bounded Interval,IEEE Trans[J].Antennas Propag,1995,43:614-622.
[10]Sahu P K,Saha R S.A New Approach Based on SemiOrthogonal B-Spline Wavelets for the Numerical Solutions of the System of Nonlinear Fredholm Integral E-quations of Second Kind[J].Comp.Appl.Math,2014,33:859-872.
[11]尹建华,任建娅.Legendre小波求解非线性分数阶Fredholm积分微分方程[J].辽宁工程技术大学学报(自然科学版),2012,31(3):405-408.
[12]Kilicman A,Zhour A A.Kronecker Operational Matrices for Fractional Calculus and Some Applications[J].Appl Math Comput,2007,187(1):250-260.
[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]黄洁,韩惠丽.应用Lengendre小波求解非线性分数阶Volterra积分微分方程[J].吉林大学学报(理学版),2014,52(7):655-660.
[5]黄洁.非线性分数阶Volterra积分微分方程的小波数值解法[D].银川:宁夏大学,2015.
[6]白如越,韩惠丽.一类种群模型的第三类Chebyshev小波解法[J].宁夏大学学报(自然科学版),2018,39(1):32-37.
[7]罗世平.来自多尺度分析的Riesz基[J].华南师范大学学报(自然科学版),2006,50(3):7-11.
[8]雷开彬,马志霞,黄天云.基于Cox-de Boor递推公式的样条函数[C].中国计算机图形学大会,2006.
[9]Goswami J C,Chan A K,Chui C K.On Solving Firstkind Integral Equations Using Wavelets on a Bounded Interval,IEEE Trans[J].Antennas Propag,1995,43:614-622.
[10]Sahu P K,Saha R S.A New Approach Based on SemiOrthogonal B-Spline Wavelets for the Numerical Solutions of the System of Nonlinear Fredholm Integral E-quations of Second Kind[J].Comp.Appl.Math,2014,33:859-872.
[11]尹建华,任建娅.Legendre小波求解非线性分数阶Fredholm积分微分方程[J].辽宁工程技术大学学报(自然科学版),2012,31(3):405-408.
[12]Kilicman A,Zhour A A.Kronecker Operational Matrices for Fractional Calculus and Some Applications[J].Appl Math Comput,2007,187(1):250-260.