三阶Emden-Fowler型微分方程的第4类Chebyshev混合函数数值解法

Numerical Solution of Third-Order Emden-Fowler Equations by the Fourth Kind of Chebyshev Hybrid Functions Method

提出了求解三阶Emden-Fowler型微分方程的第4类Chebyshev混合函数方法。通过第4类Chebyshev多项式解析形式与BPF函数相结合,构造出第4类Chebyshev混合函数。在Rieman-Liouville分数积分定义下,借助Laplace变换导出第4类Chebyshev混合函数的分数阶积分公式。利用第4类Chebyshev混合函数得出误差上界。结合配置法将三阶Emden-Fowler型微分方程转化为代数方程组进行求解。通过实例验证了该方法的有效性与可行性。

In this paper,a fourth kind of chebyshev hybrid function method for solving three-order Emden-Fowler differential equations is proposed.By combining the analytic form of the fourth Chebyshev polynomial with the BPF function,the fourth Chebyshev hybrid function is constructed.Under the definition of Rieman-Liouville fractional integral,the exact expression of fractional integral of the fourth kind of Chebyshev hybrid function is derived by means of Laplace transform.The upper bound of error is obtained by using the fourth Chebyshev hybrid function.Combined with the configuration method,the third-order Emden-Fowler differential equations are transformed into algebraic equations for solving.The reliability and effectiveness of the method are verified by examples.