Numerical solution of problems on unbounded domains. a review
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Applied Numerical Mathematics
Design of Absorbing Boundary Conditions for Schrödinger Equations in $\mathbbR$d
SIAM Journal on Numerical Analysis
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Finite difference/spectral approximations for the time-fractional diffusion equation
Journal of Computational Physics
A Space-Time Spectral Method for the Time Fractional Diffusion Equation
SIAM Journal on Numerical Analysis
A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
Numerical Blow-up of Semilinear Parabolic PDEs on Unbounded Domains in R2
Journal of Scientific Computing
Journal of Computational Physics
Computation of some unsteady flows over porous semi-infinite flat surface
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
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In this paper, for a class of fractional sub-diffusion equations on a space unbounded domain, firstly, exact artificial boundary conditions, which involve the time-fractional derivatives, are derived using the Laplace transform technique. Then the original problem on the space unbounded domain is reduced to the initial-boundary value problem on a space bounded domain. Secondly, an efficient finite difference approximation for the reduced initial-boundary problem on the space bounded domain is constructed. Different from the method of order reduction used in [37] for the fractional sub-diffusion equations on a space half-infinite domain, the presented difference scheme, which is more simple than that in the previous work, is developed using the direct discretization method, i.e. the approximate method of considering the governing equations at mesh points directly. The stability and convergence of the scheme with numerical accuracy O(@t^2^-^@c+h^2) are proved by means of discrete energy method and Sobolev imbedding inequality, where @c is the order of time-fractional derivative in the governing equation, @t and h are the temporal stepsize and spatial stepsize, respectively. Thirdly, a compact difference scheme for the case of @c=