𝔖 Bobbio Scriptorium
✦   LIBER   ✦

TLM-based solutions of the Klein–Gordon equation (Part I)

✍ Scribed by William J. O'Connor; Fergus J. Clune

Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
123 KB
Volume
14
Category
Article
ISSN
0894-3370

No coin nor oath required. For personal study only.

✦ Synopsis

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 to solving the Klein–Gordon equation that arises in Quantum Mechanics and in the dynamics of an elastically anchored vibrating string. In Part I, two novel, TLM‐based algorithms are presented and verified. By considering them as solving a special case of the more general ‘forced’ wave equation, they illustrate how, with care, the TLM algorithm can be adapted to model a wide range of effects. Copyright © 2001 John Wiley & Sons, Ltd.

📜 SIMILAR VOLUMES

TLM-based solutions of the Klein–Gordon
TLM-based solutions of the Klein–Gordon equation (Part II)
✍ William J. O'Connor; Fergus J. Clune 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 67 KB 👁 1 views

## 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 resp

On the numerical solution of the Klein-G
On the numerical solution of the Klein-Gordon equation
✍ A.G. Bratsos 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 203 KB 👁 1 views

## 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

A posteriori error estimation for finite
A posteriori error estimation for finite element solutions of Helmholtz’ equation. part I: the quality of local indicators and estimators
✍ I. Babuška; F. Ihlenburg; T. Strouboulis; S. K. Gangaraj 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 271 KB 👁 3 views

This paper contains a first systematic analysis of a posteriori estimation for finite element solutions of the Helmholtz equation. In this first part, it is shown that the standard a posteriori estimates, based only on local computations, severely underestimate the exact error for the classes of wav

A posteriori error estimation for finite
A posteriori error estimation for finite element solutions of Helmholtz' equation—Part II: estimation of the pollution error
✍ I. Babuška; F. Ihlenburg; T. Strouboulis; S. K. Gangaraj 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 319 KB 👁 2 views

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