第六类正交Chebyshev多项式混合Block-Pulse函数求解分数阶Lane-Emden微分方程

doi:10.12288/szjs.s2022-0818

数值计算与计算机应用 ›› 2023, Vol. 44 ›› Issue (1): 95-112.DOI: 10.12288/szjs.s2022-0818

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第六类正交Chebyshev多项式混合Block-Pulse函数求解分数阶Lane-Emden微分方程

黄英杰, 周凤英, 许小勇

东华理工大学理学院, 南昌 330013

收稿日期:2022-01-19 出版日期:2023-03-14 发布日期:2023-03-16
基金资助:
国家自然科学基金（11601070）；江西省自然科学基金（20202BABL201006）；东华理工大学博士科研启动项目（DHBK2019213）资助.

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黄英杰, 周凤英, 许小勇. 第六类正交Chebyshev多项式混合Block-Pulse函数求解分数阶Lane-Emden微分方程[J]. 数值计算与计算机应用, 2023, 44(1): 95-112.

Huang Yingjie, Zhou Fengying, Xu Xiaoyong. USING THE SIXTH KIND OF ORTHOGONAL CHEBYSHEV POLYNOMIAL MIXED BLOCK PULSE FUNCTION TO SOLVE FRACTIONAL LANE-EMDEN DIFFERENTIAL EQUATIONS[J]. Journal on Numerica Methods and Computer Applications, 2023, 44(1): 95-112.

USING THE SIXTH KIND OF ORTHOGONAL CHEBYSHEV POLYNOMIAL MIXED BLOCK PULSE FUNCTION TO SOLVE FRACTIONAL LANE-EMDEN DIFFERENTIAL EQUATIONS

Huang Yingjie, Zhou Fengying, Xu Xiaoyong

School of Sciences, East China University of Technology, Nanchang 330013, China

Received:2022-01-19 Online:2023-03-14 Published:2023-03-16

基于第六类正交Chebyshev多项式混合Block-Pulse函数，获得了一种求解分数阶Lane-Emden型微分方程数值解的数值方法.混合函数由第六类正交Chebyshev多项式与Block-Pulse函数构成.在Rieman-Liouville分数阶积分定义下，利用Laplace变换导出了混合函数的分数阶积分公式表达式.利用混合函数积分公式以及结合有效的配点法，将具有边界条件的分数阶Lane-Emden微分方程转化成一个代数方程组，再运用迭代法进行数值求解.同时，还给出了混合函数展开的一致收敛性分析和误差估计.文中数值算例和数值结果验证了该方法的有效性和准确性.

关键词： 分数阶Lane-Emden微分方程, 第六类正交Chebyshev多项式, Block-Pulse函数, Rieman-Liouville分数阶积分

Based on the sixth kind of orthogonal Chebyshev polynomial mixed block pulse function, a numerical method for solving the numerical solutions of fractional Lane-Emden differential equations is obtained. The mixed functions consist of the sixth kind of orthogonal Chebyshev polynomials and block pulse functions. Under the definition of Rieman-Liouville fractional order integral, the fractional integral formulas of mixed functions are derived by Laplace transform. Using the mixed functions integral formulas and the effective collocation method, the fractional Lane-Emden differential equation with boundary conditions is transformed into an algebraic equation system, and then the iterative method is used for numerical solution. At the same time, the uniform convergence analysis and error estimation of mixed function expansion are also given. Numerical examples and results verify the effectiveness and accuracy of the method.

Key words: Fractional Lane-Emden differential equations, The sixth kind of orthogonal Chebyshev polynomial, Block-Pulse function, Rieman-Liouville fractional integral

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第六类正交Chebyshev多项式混合Block-Pulse函数求解分数阶Lane-Emden微分方程

USING THE SIXTH KIND OF ORTHOGONAL CHEBYSHEV POLYNOMIAL MIXED BLOCK PULSE FUNCTION TO SOLVE FRACTIONAL LANE-EMDEN DIFFERENTIAL EQUATIONS

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