Bernstein多项式求一类变分数阶微分方程数值解

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

为求变分数阶微分方程的数值解,应用Bernstein多项式求解一类线性、非线性变分数阶微分方程.结合Bernstein多项式,求得3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该线性或者非线性方程组,通过求解方程组,从而得到数值解.数值算例验证了本方法的高度可行性和准确性.

In order to use Bemstein polynomials to seek the numerical solution of a class of linear including nonlinear variable order fractional differential equation, this paper derives three different kinds of operational matrixes with Bemstein polynomials. The initial equation is transformed into the products of several dependent matrixes which can also be regarded as the system of linear or nonlinear equations after dispersing the variable. By solving the system of equations, the numerical solutions are acquired. Numerical examples are provided to show that the method is computationally efficient and accurate.