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(?2??+h2). The accuracy and efficiency of the scheme are checked by two numerical tests.
box-type scheme sub-diffusion equation neumann boundary conditions stability convergence energy method