A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions
Combining order reduction approach and L1 discretization, a box-type scheme is presented for solving a class of fractional sub-diffusion equation with Neumann boundary conditions. A new inner product and corresponding norm with a Sobolev embedding inequality are introduced. A novel technique is applied in the proof of both stability and convergence. The global convergence order in maximum norm is O(tau(2-alpha) + h(2)). The accuracy and efficiency of the scheme are checked by two numerical tests. (C) 2011 Elsevier Inc. All rights reserved.
box-type scheme sub-diffusion equation neumann boundary conditions stability convergence energy method