【摘要】 提出求解时间分数阶扩散方程的三次样条差分格式,证明该格式是无条件稳定的,其局部截断误差阶为O(Δt+Δx2)。该分数阶扩散方程是将一般的扩散方程中的时间一阶导数用α(0<α<1)阶导数代替所得到的。数值算例表明三次样条差分格式是有效的。更多还原

【Abstract】 A cubic spline difference scheme for solving the time fractional diffusion equation is presented.It is shown that the method is unconditional stable and the order of local truncation error O(Δt+Δx2).The fractional diffusion equation is obtained from the classical diffusion equation by replacing the first order time derivative with fractional derivative of order α(0<α<1).Finally,the numerical example shows that the presented method is effective.更多还原