摘要:
A new implicit difference approximation to solve a time fractional derivative equation is proposed.The spatial derivative is directly discretized by central difference scheme.To approxi-mate the Caputo fractional derivative,it is established by means of the quadratic interpolation ap-proximation.Using three points u(x,tn-2),u(x,tn-1),u(x,tn)for the integrand u(x,t)on each small interval[tn-1,tn](2≤n≤N),while the linear interpolation approximation is applied on the first small interval[t0,t1].Using the energy norm,the unconditional stability and convergence of the scheme are proved.Finally,a numerical experiment shows that the scheme is efficient.%针对一类时间分数阶扩散方程提出了一种新的隐式差分格式,空间导数直接采用中心差分格式离散,为了近似Caputo型时间分数阶导数,在小区间[tn-1,tn](2≤n≤N)上使用三点u(x,tn-2)、u(x,tn-1)、u(x,tn)二次插值近似u(x,t)的值,在小区间[t0,t1]上使用线性插值近似u(x,t)的值,并利用能量范数证明该格式的无条件稳定性和收敛性,最后通过数值实验验证该格式的有效性.