高阶微分方程的第3类Chebyshev小波数值解法

Numerical Solution for Higher Order Differential Equations bythe third Kind of Chebyshev Wavelet Method

提出了一种求解高阶微分方程数值解的第3类Chebyshev小波方法。通过利用位移第3类Chebyshev多项式,在Riemann-liouville分数阶定义下,借助Laplace变换推导了第3类Chebyshev小波函数分数阶积分的精确表达式,给出了小波函数逼近的误差估计。利用小波配置法,将高阶微分方程的求解问题转化为代数方程组进行求解。数值算例表明了该算法的适用性与有效性。

In this paper,a third kind of Chebyshev wavelet method for solving numerical solutions of higher order differential equations is proposed.By using the Chebyshev polynomials of the third kind of displacement and the definition of Riemann Liouville fractional order,the exact expression of fractional integral of the third kind of Chebyshev wavelet function is derived by means of Laplace transform,and the error estimate of approximation of wavelet function is given.By using wavelet collocation method,the problem of solving high-order differential equations is transformed into algebraic equations for solving.Numerical examples show the applicability and effectiveness of the algorithm.