Pii: S0168-9274(00)00061-1
نویسندگان
چکیده
We construct two variable-step linearly implicit Runge–Kutta methods of orders 3 and 4 for the numerical integration of the semidiscrete equations arising after the spatial discretization of advection–reaction–diffusion equations. We study the stability properties of these methods giving the appropriate extension of the concept of L-stability. Numerical results are reported when the methods presented are combined with spectral discretizations. Our experiments show that the methods, being easily implementable, can be competitive with standard stiffly accurate time integrators. 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.
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Pii: S0168-9274(00)00050-7
The aim of this work is to present a nonstandard linear finite element method for a planar elasticity problem. The error for the solution computed with this method is estimated with respect to H 1 ×H 1-norm and second-order convergence is shown. 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.
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We derive conservative fourthand sixth-order finite difference approximations for the divergence and gradient operators and a compatible inner product on staggered 1D uniform grids in a bounded domain. The methods combine standard centered difference formulas in the interior with new one-sided finite difference approximations near the boundaries. We derive compatible inner products for these di...
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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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We have written a program, dde23, to solve delay differential equations (DDEs) with constant delays in MATLAB. In this paper we discuss some of its features, including discontinuity tracking, iteration for short delays, and event location. We also develop some theoretical results that underlie the solver, including convergence, error estimation, and the effects of short delays on stability. Som...
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