Pii: S0168-9274(99)00114-2
نویسندگان
چکیده
This paper concerns the iterative solution of the linear system arising from the Chebyshev–collocation approximation of second-order elliptic equations and presents an optimal multigrid preconditioner based on alternating line Gauss–Seidel smoothers for the corresponding stiffness matrix of bilinear finite elements on the Chebyshev–Gauss–Lobatto grid. 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.
منابع مشابه
Pii: S0168-9274(99)00020-3
We compare several methods for sensitivity analysis of differential–algebraic equations (DAEs). Computational complexity, efficiency and numerical conditioning issues are discussed. Numerical results for a chemical kinetics problem arising in model reduction are presented. 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.
متن کاملPii: S0168-9274(99)00131-2
We study numerical integrators that contract phase space volume even when the ODE does so at an arbitrarily small rate. This is done by a splitting into two-dimensional contractive systems. We prove a sufficient condition for Runge–Kutta methods to have the appropriate contraction property for these two-dimensional systems; the midpoint rule is an example. 2000 IMACS. Published by Elsevier Sc...
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We study the error propagation of time integrators of solitary wave solutions for the regularized long wave equation, ut +ux+ 2 (u)x −uxxt = 0, by using a geometric interpretation of these waves as relative equilibria. We show that the error growth is linear for schemes that preserve invariant quantities of the problem and quadratic for ‘nonconservative’ methods. Numerical experiments are prese...
متن کاملPii: S0168-9274(99)00082-3
A fast Chebyshev–Fourier algorithm for Poisson-type equations in polar geometries is presented in this paper. The new algorithm improves upon the algorithm of Jie Shen (1997), by taking advantage of the odd–even parity of the Fourier expansion in the azimuthal direction, and it is shown to be more efficient in terms of CPU and memory. 2000 IMACS. Published by Elsevier Science B.V. All rights ...
متن کاملPii: S0168-9274(01)00134-9
A postprocessing technique to improve the accuracy of Galerkin methods, when applied to dissipative partial differential equations, is examined in the particular case of very smooth solutions. Pseudospectral methods are shown to perform poorly. This performance is studied and a refined postprocessing technique is proposed. 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.
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