Alternating direction methods for parabolic equations in two space dimensions with a mixed derivative
نویسندگان
چکیده
منابع مشابه
On Accuracy of Alternating Direction Implicit Methods for Parabolic Equations
We study accuracy of alternating direction implicit (ADI) methods for parabolic equations. The original ADI method applied to parabolic equations is a perturbation of the Crank-Nicolson di erence equation and has second-order accuracy both in space and time. The perturbation error is on the same order as the discretization error, in terms of mathematical description. However, we often observe i...
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An efficient modification by Douglas and Kim of the usual alternating directions method reduces the splitting error from O(k2) to O(k3) in time step k. We prove convergence of this modified alternating directions procedure, for the usual non-mixed Galerkin finite element and finite difference cases, under the restriction that k/h2 is sufficiently small, where h is the grid spacing. This improve...
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In this paper, we propose an efficient alternating direction implicit (ADI) Galerkin method for solving the time-fractional partial differential equation with damping, where the fractional derivative is in the sense of Caputo with order in (1, 2). The presented numerical scheme is based on the L2-1σ method in time and the Galerkin finite element method in space. The unconditional stability and ...
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ژورنال
عنوان ژورنال: The Computer Journal
سال: 1970
ISSN: 0010-4620,1460-2067
DOI: 10.1093/comjnl/13.1.81