| Legendre小波求解非线性分数阶Fredholm积分微分方程 |
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| 引用本文： | 尹建华,任建娅,仪明旭.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. |
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| 作者姓名： | 尹建华 任建娅 仪明旭 |
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| 作者单位： | 1. 河北民族师范学院数学与计算机系,河北承德,067000
2. 燕山大学理学院,河北秦皇岛,066004 |
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| 基金项目： | 河北省自然科学基金资助项目(A2011205092) |
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| 摘 要： | 为了求解非线性分数阶Fredholm积分微分方程的数值解,通过Legendre多项式,得出了Legendre小波,并由block pulse函数给出了Legendre小波的分数阶积分算子矩阵,利用block pulse函数与Legendre小波的积分算子矩阵的性质将非线性分数阶Fredholm积分微分方程转化为非线性代数方程组,进而可以求得原积分微分方程的数值解.结果表明:随着点数的增多,数值解的精度也越来越高.文中给出的算例表明了该方法的可行性和有效性.
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| 关 键 词： | Legendre多项式 Legendre小波 Fredholm积分微分方程 非线性 block pulse函数 算子矩阵 分数阶微分 数值解 |
Legendre wavelet method for solving nonlinear Fredholm integro-differential equations of fractional order |
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| YIN Jianhua
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REN Jianya
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YI Mingxu.Legendre wavelet method for solving nonlinear Fredholm integro-differential equations of fractional order[J].Journal of Liaoning Technical University (Natural Science Edition),2012,31(3):405-408. |
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| Authors: | YIN Jianhua REN Jianya YI Mingxu |
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| Institution: | 1.Department of Mathematics and Computer Science,Hebei Teachers College for Nationalities, Chengde 067000,China;2.College of Science,Yanshan University,Qinghuangdao 066004,China) |
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| Abstract: | In order to obtain a numerical solution for nonlinear Fredholm integro-differential equations of fractional order,this study obtains Legendre wavelet through Legendre polynomial.Subsequently,it derives the integral operational matrix of fractional order of Legendre wavelet through block pulse functions.Furthermore,the nonlinear Fredholm integro-differential equations are transformed into a nonlinear system of algebraic equations using the properties of block pulse functions and the integral operational matrix of fractional order of Legendre wavelet.Therefore,the numerical solution of original equations can be obtained.The results show that with the increase of points,the precision of numerical solution is increasing.The numerical example demonstrates the effectiveness and feasibility of the method proposed. |
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| Keywords: | Legendre polynomial Legendre wavelet Fredholm integro-differential equations nonlinear block pulse function operational matrix fractional derivatives numerical solution |
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