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Finite difference
About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.
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TL;DR: In this paper, a two-dimensional mathematical model was theoretically developed to predict the temperature polarization profile of direct contact membrane distillation (DCMD) processes and a concurrent flat-plate device was designed to verify the theoretical prediction of pure water productivity on saline water desalination.
159 citations
TL;DR: In this paper, a numerical method for transmitting waves out of an artificial boundary is presented, which is applicable to linear two-or three-dimensional wave problems with a time-stepping algorithm and a convex artificial boundry.
159 citations
TL;DR: Finite difference methods for the Gross-Pitaevskii equation with an angular momentum rotation term in two and three dimensions are analyzed and error bounds on the errors between the mass and energy in the discretized level and their corresponding continuous counterparts are derived.
Abstract: We analyze finite difference methods for the Gross-Pitaevskii equation with an angular momentum rotation term in two and three dimensions and obtain the optimal convergence rate, for the conservative Crank-Nicolson finite difference (CNFD) method and semi-implicit finite difference (SIFD) method, at the order of O(h2 + τ2) in the l2-norm and discrete H1-norm with time step τ and mesh size h. Besides the standard techniques of the energy method, the key technique in the analysis for the SIFD method is to use the mathematical induction, and resp., for the CNFD method is to obtain a priori bound of the numerical solution in the l∞-norm by using the inverse inequality and the l2-norm error estimate. In addition, for the SIFD method, we also derive error bounds on the errors between the mass and energy in the discretized level and their corresponding continuous counterparts, respectively, which are at the same order of the convergence rate as that of the numerical solution itself. Finally, numerical results are reported to confirm our error estimates of the numerical methods.
159 citations
TL;DR: A jump-diffusion model for a single-asset market is considered and results showing the quadratic convergence of the methods are given for Merton's model and Kou's model.
158 citations
TL;DR: In this paper, ten different finite-difference schemes for numerical integration of the primitive equations for the free-surface model are tested for stability and accuracy, and the integrations show that the quadratic conservative and the total energy conservative schemes are more stable than the usual second-order conservative scheme.
Abstract: Ten different finite-difference schemes for the numerical integration of the primitive equations for the free-surface model are tested for stability and accuracy. The integrations show that the quadratic conservative and the total energy conservative schemes are more stable than the usual second-order conservative scheme. But the most stable schemes are those in which the finite-difference approximations to the advection terms are calculated over nine grid points in space and therefore contain a form of smoothing, and the generalized Arakawa scheme, which for nondivergent flow conserve mean vorticity, mean kinetic energy, and mean square vorticity. If the integrations are performed for more than 3 days, it is shown that more than 15 grid points per wavelength are probably needed to describe with accuracy the movement and development of the shortest wave that initially is carrying a significant part of the energy. This is true even if a fourth-order scheme in space is used. Long-term integrations ...
158 citations