in this paper, a new numerical method for solving time-fractional diffusion equations is introduced. for this purpose, finite difference scheme for discretization in time and chebyshev collocation method is applied. also, to simplify application of the method, the matrix form of the suggested method is obtained. illustrative examples show that the proposed method is very efficient and accurate.

Abstract We consider numerical boundary conditions for high order finite difference schemes for solving convection-diffusion equations on arbitrary geometry. The two main difficulties for numerical boundary conditions in such situations are: (1) the wide stencil of the high order finite difference operator requires special treatment for a few ghost points near the boundary; (2) the physical bou...

We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which, correspondingly, can not be viewed as self-affine random processes possessing a unique Hurst exponent. We prove the positivity of the solutions of the proposed equ...

We show that lattice dynamical systems naturally arise on infinite-dimensional invariant manifolds of reaction-diffusion equations with spatially periodic diffusive fluxes. The result connects wave pinning phenomena in lattice differential equations and in reaction-diffusion equations in inhomogeneous media. The proof is based on a careful singular perturbation analysis of the linear part, wher...

Scientific computations for diffusion equations and ANNs (Artificial Neural Networks) are data intensive tasks accompanied by heavy memory access; on the other hand, their computational complexities are relatively low. Thus, this type of tasks naturally maps onto SIMD (Single Instruction Multiple Data stream) parallel processing with distributed memory. This paper proposes a high performance ac...

Oxygen is an essential part of the living organism. It is transported from blood to the body tissue by the systematic circulation and large part of it is stored in the blood flowing in capillaries. In this work we discuss a mathematical model for oxygen transport in tissues. The governing equations are established assuming that the blood is flowing along a co-axial cylindrical capillary inside ...