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Finite difference method

About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.


Papers
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Journal ArticleDOI
TL;DR: In this article, numerical perturbation calculations on Be and C2+ were performed starting from a model space consisting of the two strongly interacting configurations 1s22s2 and 1s 22p2.
Abstract: We report here numerical perturbation calculations on Be and C2+ starting from a model space consisting of the two strongly interacting configurations 1s22s2 and 1s22p2. We use numerically represented radial pair functions which are solutions of a system of coupled differential equations obtained by a finite difference method. By iterating the system of pair equations the most important correlation effects are included to all orders. This is demonstrated for C2+, where excitation energies for the 2p2 levels are obtained with an accuracy better than 1% or 0.2 eV. For Be only second-order results are reported. Here the iterative scheme does not converge, probably due to the presence of intruder states of the type 2sns 1S, which lie between the two 1S states originating from the model space. The second-order calculation with the two-configurational model space and orbitals generated in the 1s2 Hertree-Fock core yields 93.6% of the correlation energy, compared to 80.9% for a similar calculation using a model space with only the ground-state configuration 1s22s2 and orbitals generated in the Hartree-Fock potential of that configuration.

116 citations

Journal ArticleDOI
TL;DR: Numerical stability and optimal error estimate O ( k Δ 2 - α + h r + 1 + H 2 r + 2 ) in L 2 -norm are proved for the two-grid scheme, where k Δ, h and H are the time step size, coarse gridMesh size, and fine grid mesh size, respectively.
Abstract: In this article, we develop a two-grid algorithm based on the mixed finite element (MFE) method for a nonlinear fourth-order reaction-diffusion equation with the time-fractional derivative of Caputo-type. We formulate the problem as a nonlinear fully discrete MFE system, where the time integer and fractional derivatives are approximated by finite difference methods and the spatial derivatives are approximated by the MFE method. To solve the nonlinear MFE system more efficiently, we propose a two-grid algorithm, which is composed of two steps: we first solve a nonlinear MFE system on a coarse grid by nonlinear iterations, then solve the linearized MFE system on the fine grid by Newton iteration. Numerical stability and optimal error estimate O ( k Δ 2 - α + h r + 1 + H 2 r + 2 ) in L 2 -norm are proved for our two-grid scheme, where k Δ , h and H are the time step size, coarse grid mesh size, and fine grid mesh size, respectively. We implement the two-grid algorithm, and present the numerical results justifying our theoretical error estimate. The numerical tests also show that the two-grid method is much more efficient than solving the nonlinear MFE system directly.

116 citations

Journal ArticleDOI
TL;DR: In this paper, numerical values for the transient velocity field, temperature field, and local heat transfer coefficient were obtained by solving the partial differential equations describing the conservation of mass, momentum, and energy on an IBM-704 computer with finite difference methods.
Abstract: Numerical values are presented for the transient velocity field, temperature field, and local heat transfer coefficient. These results were obtained by solving the partial differential equations describing the conservation of mass, momentum, and energy on an IBM-704 computer with finite difference methods in time-dependent form. The computed values for short times agree very well with the analytical solution for conduction only, and the limiting values for long time agree well with previous solutions for the steady state. The existence of a temporal minimum in the heat transfer coefficient is confirmed. The time required for the heat transfer coefficient to approach its steady state is shown to be less than previously predicted.

116 citations

Book
01 Jan 1975
TL;DR: In this article, the theory and applications of the analytical techniques used in finding stresses in highway and other bridge decks are discussed and an approximate method of determination of bending moments for initial design is described.
Abstract: The book presents the theory and applications of the analytical techniques used in finding stresses in highway and other bridge decks. Current trends in bridge design and construction are discussed and are followed by the various analytical methods. The plate method is dealt with, initially by the basic derivation and solution of the plate equation. A chapter is devoted to the determination of the equivalent plate rigidities of various representative types of bridge deck. An approximate method of determination of bending moments for initial design is described. Various special applications of orthotropic plate theory are covered and the finite difference method for plates is described, including a summary of the dynamic relaxation method. The last four chapters deal with the stiffness method and its application: grillage and space frame analysis, the folded plate method, the finite element method, and the finite strip method. The book is intended for use by bridge designers and students with a particular interest in bridge engineering. /TRRL/

115 citations

Journal ArticleDOI
TL;DR: In this article, a model has been established for deep borehole heat exchanger (DBHE) with coaxial tubes, considering coupled heat transfer in the tubes and surrounding subsurface, and an algorithm for direct solution of resulted algebraic equation set is used so as to achieve very efficient computation.

115 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023125
2022320
2021724
2020681
2019667
2018694