• 论文 •

### 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

1. 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.

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

1. School of Sciences, East China University of Technology, Nanchang 330013, China
• Received:2022-01-19 Online:2023-03-14 Published:2023-03-16

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.

MR(2010)主题分类:

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