再生核移位勒让德基函数法求解分数阶微分方程

Reproducing Kernel Shifted Legendre Basis Function Method for Solving the Fractional Differential Equations

该文以再生核理论为基础,用移位Legendre多项式作为基函数构造了一个新的再生核空间,并给出了该空间下的再生核函数.与经典的再生核函数有所不同的是该空间下的再生核函数不再是分段函数,因此可以减小分数阶算子作用在核函数上时的计算量,使近似解更为精确.数值算例表明该方法的有效性.

Based on the theory of the reproducing kernel,this paper constructed a new reproducing kernel space and the reproducing kernel function of the space is given by using the shifted Legendre polynomials as the basis function.It is different from former that this function is no longer a piecewise function,so when the fractional operator is used on the kernel function,the computation is reduced.Thus the approximate solution is more accurate.Finally,the numerical examples illustrate the validity of the method.