小波法求解分数阶微分方程的误差估计

Error estimation of wavelet method to solve fractional differential equations

针对求解分数阶微分方程数值解和所得结果误差大小问题.采用Haar小波分数阶积分算子矩阵方法,得到一类变系数分数阶微分方程数值解.利用所得算子矩阵将原分数阶微分方程转化为代数方程组,进而便于编程求解.讨论算法的误差分析,给出相应的误差估计式,并证明该算法是收敛的.结果表明:随着点数的增多,所得数值解与精确解的误差也越来越小.最后,数值算例验证了方法的有效性以及理论分析的正确性.

Focusing on the problem of the numerical solution of fractional differential equations and the errors of the obtained result,this study provided the numerical solutions to a class of fractional differential equations with variable coefficient by using Haar wavelets operational matrix of fractional order integration,and transformed the initial fractional differential equations into a system of algebraic equations by using the obtained operational matrix,and then implemented the solution by software.This paper mainly discussed the error analysis of the method and have obtained the error estimation,and also proved that the method is convergent.The results show that the more points,the higher precision between the numerical solution and the exact solution.Finally,numerical example is provided to verify the validity of the method and the correctness of the theoretical analysis.