Pii: S0168-9274(99)00140-3
نویسنده
چکیده
In this paper we consider numerical methods for a singularly perturbed reaction–diffusion problem with a discontinuous source term. We show that such a problem arises naturally in the context of models of simple semiconductor devices. We construct a numerical method consisting of a standard finite difference operator and a non-standard piecewise-uniform mesh. The mesh is fitted to the boundary and interior layers that occur in the solution of the problem. We show by extensive computations that, for this problem, this method is parameteruniform in the maximum norm, in the sense that the numerical solutions converge in the maximum norm uniformly with respect to the singular perturbation parameter. 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)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(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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متن کاملPii: S0168-9274(99)00148-8
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...
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