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Your search keyword '"Higher Order Methods"' showing total 2 results
Start Over Descriptor "Higher Order Methods" Publisher elsevier
2 results on '"Higher Order Methods"'

1. An explicit high order method for fractional advection diffusion equations

Author

Ercília Sousa

Subjects
FTCS scheme, Finite differences, Numerical Analysis, Fractional differential equations, Physics and Astronomy (miscellaneous), Advection, Applied Mathematics, Numerical analysis, Mathematical analysis, Finite difference, Higher order methods, Advection diffusion equations, 16. Peace & justice, Computer Science Applications, Fractional calculus, Computational Mathematics, Rate of convergence, Modeling and Simulation, Volume of fluid method, Diffusion (business), Mathematics
Abstract

We propose a high order explicit finite difference method for fractional advection diffusion equations. These equations can be obtained from the standard advection diffusion equations by replacing the second order spatial derivative by a fractional operator of order α with 1 < α ? 2 . This operator is defined by a combination of the left and right Riemann-Liouville fractional derivatives. We study the convergence of the numerical method through consistency and stability. The order of convergence varies between two and three and for advection dominated flows is close to three. Although the method is conditionally stable, the restrictions allow wide stability regions. The analysis is confirmed by numerical examples.

Published
2014

2. Subsampling and inpainting approaches for electron tomography.

Author

Sanders T and Dwyer C

Abstract

With the aim of addressing the issue of sample damage during electron tomography data acquisition, we propose a number of new reconstruction strategies based on subsampling (which uses only a subset of a full image) and inpainting (recovery of a full image from subsampled one). We point out that the total-variation (TV) inpainting model commonly used to inpaint subsampled images may be inappropriate for 2D projection images of typical TEM specimens. Thus, we propose higher-order TV (HOTV) inpainting, which accommodates the fact that projection images may be inherently smooth, as a more suitable image inpainting scheme. We also describe how the HOTV method can be extended to 3D, a scheme which makes use of both image data and sinogram data. Additionally, we propose gradient subsampling as a more efficient scheme than random subsampling. We make a rigorous comparison of our proposed new reconstruction schemes with existing ones. The new schemes are demonstrated to perform better than or as well as existing schemes, and we show that they outperform existing schemes at low subsampling rates., (Copyright © 2017 Elsevier B.V. All rights reserved.)

Published
2017
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