The stability and convergence analysis of finite difference methods for the fractional neutron diffusion equation

For the time-fractional neutron diffusion equation with a Caputo derivative of order α∈(0,12) , we give the optimal error bounds of L1-type schemes under the spatial L^∞ -norm with lower regularity solution than typical |∂tlu(x,t)|≤C(1+t2α-l),l=0,1,2 , where 2α is the highest order of the time-fractional derivative. The unique solvability and the numerical stability of schemes will be exported via a simple restriction of coefficients with non-uniform time steps τn<π4 . The truncation error of term D0,t2α with low regularity |∂tlu(x,t)|≤C(1+tα-l),l=0,1,2 , and the global error of full discretizations will be given. In addition, several numerical examples will be shown to test our theoretical results.