Legendre多项式法求一类变阶数分数阶微分方程数值解  

Numerical Solution for a Class of Variable Order Fractional Differential Equation Using Legendre Polynomials

作　　者：李志文[1] 尹建华[1] 耿万海[2] 

机构地区：[1]河北民族师范学院,河北承德067000 [2]燕山大学理学院,河北秦皇岛066004

出　　处：《应用数学》2015年第3期609-616,共8页Mathematica Applicata

基　　金：国家自然科学基金(61176089)

摘　　要：本文利用Legendre多项式求解一类变分数阶微分方程.结合Legendre多项式,给出三种不同类型的微分算子矩阵.通过微分算子矩阵,将原方程转化一系列矩阵的乘积.最后离散变量,将矩阵的乘积转化为代数方程组,通过求解方程组,从而得到原方程的数值解.数值算例验证了本方法的高度可行性和准确性.In this paper, we use Legendre polynomials to solve the numerical solution of a class of variable order fractional differential equations. We derive three different kinds of operational matrixes with Legendre polynomials, so the initial equation is transformed into the products of several dependent matrixes which can also be regarded as a system of equations after dispersing the variable. By solving the system of equations, the numerical solutions are obtained. Numerical examples are provided to show that the method is computationally efficient and accurate.

关 键 词：变分数阶微分方程 LEGENDRE多项式 算子矩阵 数值解 绝对误差 

分 类 号：O241.8[理学—计算数学]