第六类Chebyshev小波配置法求分数阶微分方程数值解

The Sixth Kind of Chebyshev Wavelet Collocation Method for Numerical Solutions of Fractional Differential Equations

基于第六类Chebyshev小波配置法,提出一种求解分数阶微分方程数值解的数值方法。利用平移的第六类Chebyshev多项式,在Riemann-Liouville分数阶定义下,获得了第六类Chebyshev小波函数的分数阶积分公式的精确表达式。利用积分公式,结合有效配置法,将分数阶微分方程的求解问题转化为代数方程组进行求解。同时,给出了第六类Chebyshev小波函数展开逼近的一致收敛性分析和L2范数意义下的误差估计。通过数值算例验证该算法的适用性与有效性。

Based on the sixth kind of Chebyshev wavelet collocation method,a numerical method for solving fractional differential equations is proposed.By using the shifted sixth kind of Chebyshev polynomials and under the definition of Riemann-Liouville fractional order,the exact expressions of the fractional order integral formulas of the sixth kind of Chebyshev wavelet functions are obtained.Using the integral formulas together with the effective collocation method,the problem of solving fractional differential equations is transformed into algebraic equations.The uniform convergence analysis of the expansion of the sixth kind of Chebyshev wavelet functions and error estimation in the sense of L 2 norm are given.Numerical examples show the applicability and effectiveness of the algorithm.