## Abstract The transmission line matrix (TLM) method has become well established as a numerical solution scheme for wave problems in electromagnetics and, to a lesser extent, in acoustics and mechanics. It has also been applied to diffusion/heat‐conduction problems. Here the technique is extended
TLM-based solutions of the Klein–Gordon equation (Part II)
✍ Scribed by William J. O'Connor; Fergus J. Clune
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 67 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0894-3370
- DOI
- 10.1002/jnm.452
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✦ Synopsis
Abstract
In Part I, two TLM‐based solutions were presented for the Klein–Gordon Equation in its basic form, with the TLM pulses representing the primary variable. In Part II, two further approaches are presented in which the TLM pulses now represent derivatives of the primary variable, with respect to either space or time. As in Part I, the two solution schemes were verified symbolically and numerically. They illustrate further ways to extend the power of TLM beyond its traditional application areas. Some of these areas are discussed briefly. Copyright © 2002 John Wiley & Sons, Ltd.
📜 SIMILAR VOLUMES
## Abstract A predictor–corrector (P–C) scheme based on the use of rational approximants of second‐order to the matrix‐exponential term in a three‐time level reccurence relation is applied to the nonlinear Klein‐Gordon equation. This scheme is accelerated by using a modification (MPC) in which the
In part I of this investigation, we proved that the standard a posteriori estimates, based only on local computations, may severely underestimate the exact error for the classes of wave-numbers and the types of meshes employed in engineering analyses. We showed that this is due to the fact that the