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In this paper, we consider the numerical solution of the time fractional diffusion equation. Essentially, the time fractional diffusion equation differs from the standard diffusion equation in the time derivative term. In the former case, the first-order time derivative is replaced by a fractional derivative, making the problem global in time. We propose a(More)
Numerical methods for solving the continuum model of the dynamics of the molecularbeam epitaxy (MBE) require very large time simulation, and therefore large time steps become necessary. The main purpose of this work is to construct and analyze highly stable time discretizations which allow much larger time step than that for a standard implicitexplicit(More)
The Cable equation has been one of the most fundamental equations for modeling neuronal dynamics. In this paper, we consider the numerical solution of the fractional Cable equation, which is a generalization of the classical Cable equation by taking into account the anomalous diffusion in the movement of the ions in neuronal system. A schema combining a(More)
The complete sequence of orange homologous capsanthin/capsorubin synthase gene is 3788 bp long with a coding sequence of 1512 bp, which encodes a polypeptide of 503 amino acids. The 5' upstream sequence is 1721 bp long and the 3' downstream sequence is 555 bp long. The amino acid sequence of this gene is 78% and 69% identical to the genes from carrot and(More)
We propose and analyze spectral direction splitting schemes for the incompressible Navier-Stokes equations. The schemes combine a Legendre-spectral method for the spatial discretization and a pressure-stabilization/direction splitting scheme for the temporal discretization, leading to a sequence of one-dimensional elliptic equations at each time step while(More)
Abstract. This paper proposes a parallel in time (also called time parareal) method to solve Volterra integral equations of the second kind. The parallel in time approach follows the spirit of the domain decomposition that consists of breaking the domain of computation into subdomains and solving iteratively the subproblems in a parallel way. To obtain a(More)
A mixed spectral method is proposed and analyzed for the Stokes problem in a semi-infinite channel. The method is based on a generalized Galerkin approximation with Laguerre functions in the x direction and Legendre polynomials in the y direction. The well-posedness of this method is established by deriving a lower bound on the inf-sup constant. Numerical(More)