Results 261 to 270 of about 79,648 (296)

On Difference Methods for Parabolic Equations and Alternating Direction Implicit Methods for Elliptic Equations

IBM Journal of Research and Development, 1967
Some aspects are discussed of the development of the theory of difference approximations to parabolic equations in its relation to the basic development of difference methods for hyperbolic and elliptic equations by Courant, Friedrichs and Lewy, Math. Ann. 100, 32 (1928).
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Accuracy of the general peaceman and Rachford alternating direction implicit method

International Communications in Heat and Mass Transfer, 1996
Abstract In this paper, the truncation error of the general Peaceman and Rachford alternating direction implicit (ADI) method in a N-dimensional space was derived by using the Taylor-series-expansion approach. The formulation of this truncation error is TE= 2−N 2N 2 ∑ i =l N ∑ j=l N ∂ 4 θ ∂η 2 i η 2 j ...
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An alternating direction implicit method for solving the shallow water equations

Journal of Computational Physics, 1971
Abstract An alternating direction implicit difference scheme is applied to the shallow water equations on a β-plane. Unconditional stability of the scheme is proved for the linearized equations. For each time step a number of nonlinear systems of algebraic equations must be solved. Different iteration methods for doing this are discussed, and a quasi-
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Micromagnetic simulation using the dynamic alternating direction implicit method

Journal of Magnetism and Magnetic Materials, 1998
Abstract We have developed a 3-D micromagnetic algorithm using finite-differences and the iterative matrix solution method, dynamic alternating direction implicit (DADI), for the magnetostatic potential equation. As in previous work, the magnetization is integrated in time toward equilibrium with the Landau–Lifshitz–Gilbert (LLG) equation.
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Critical analysis of the alternating direction implicit method of aquifer analysis

Journal of Hydrology, 1974
Abstract The alternating direction implicit method, when used for aquifer analysis, is liable to lead to erroneous results. By a careful examination of the effect of various factors, such as external boundaries, variable mesh intervals, internal boundaries with fixed heads, re-entrant boundaries and leakage, the occasions when these errors are ...
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The smoothing properties of the alternating direction implicit method in multigrid iterations

Applied Numerical Mathematics, 1987
This paper uses local mode analysis to assess the performance of a multigrid method using an ADI as a smoother for solving the Laplace and biharmonic equations. The analysis shows that, in this context, ADI compares favorably to Gauss-Seidel using lexicographic ordering.
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Tensor Product Analysis of Alternating Direction Implicit Methods

Journal of the Society for Industrial and Applied Mathematics, 1965
Lynch, R. E., Rice, J. R., Thomas, D. H.
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Another Alternating-Direction-Implicit Method

Journal of the Society for Industrial and Applied Mathematics, 1963
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A finite volume–alternating direction implicit method for the valuation of American options under the Heston model

International Journal of Computer Mathematics, 2020
Jiacheng Cai
exaly  

A generalized alternating direction implicit method for transient thermal simulation of 2-D structures with locally refined grids

Numerical Heat Transfer, Part B: Fundamentals, 2023
Junfa Mao
exaly