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Practical stability analysis of finite difference equations by the matrix method

✍ Scribed by James Sucec

Publisher
John Wiley and Sons
Year
1987
Tongue
English
Weight
517 KB
Volume
24
Category
Article
ISSN
0029-5981

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✦ Synopsis

It is shown how the various norms of the coefficient matrix of a set of finite difference equations can, in many cases, be employed in an easy, straightforward fashion to find sufficient conditions for stability in situations involving non-periodic boundary conditions and variable coefficients. With the aid of the easily computed norms, particularly the infinite norm. one docs not have to rely on the necessary condition provided by the spectral radius, which has been the main basis of criticism of the matrix method in the past.

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✍ Rob F. Remis πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 86 KB

In this paper we give a necessary and sufficient condition for the stability of the finite-difference time-domain method (FDTD method). This is an explicit time stepping method that is used for solving transient electromagnetic field problems. A necessary (but not a sufficient) condition for its sta