应用Bernstein多项式求解一类变分数阶微分方程

Numerical solution for a class of variable order fractional differential equation by Bernstein polynomials

文章应用Bernstein多项式求解一类变分数阶微分方程,结合Bernstein多项式的一阶微分算子矩阵、分数阶微分算子矩阵,通过离散变量,将原方程转化为线性方程组,通过解该线性方程组,进而得到数值解。数值算例验证了该方法的高度可行性和准确性。

In this paper ,Bernstein polynomials are used to seek the numerical solution of a class of variable order fractional differential equation .With the differential operator matrix of first order and the fractional operator matrix of Bernstein polynomials ,the initial equation is transformed into the products of several dependent matrixes which can also be regarded as the system of linear equations after dispersing the variable .By solving the system of linear equations , the numerical solutions are acquired .Numerical examples are provided to show that the method is computationally efficient and ac‐curate .