Numerical Partial Differential Equations

Thomas, J. W.

doi:10.1007/978-1-4612-0569-2

Cited by 166 publications

(93 citation statements)

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“…(3) into the difference equations, such as the update equations in Yee's FDTD, we obtain the so-called amplification polynomial equation, from which the amplification factor can be found. Once the stability is proved, the amplification factor is then used to obtain the general dissipation and dispersion relation [13].…”

Section: Fourier Mode From the Difference Equationsmentioning

confidence: 99%

Numerical validation of dispersion relations using a cylindrical wave for 2D FDTD methods

Sun¹,

Trueman²

2004

Micro & Optical Tech Letters

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The numerical dispersion of a proposed new FDTD scheme is often evaluated and compared with that of well-established FDTD methods. Because there may be a theoretical deficiency in the dispersion analysis, numerical experimentation is often used to validate the dispersion relation. This paper describes the "matching method" for validation using a cylindrical wave in the two-dimensional (2D) case. The matching method is demonstrated by evaluating the numerical dispersion of Yee's FDTD and ADI-FDTD. The result is compared with

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Section: Fourier Mode From the Difference Equationsmentioning

confidence: 99%

Numerical validation of dispersion relations using a cylindrical wave for 2D FDTD methods

Sun¹,

Trueman²

2004

Micro & Optical Tech Letters

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“…With the use of the efficient Thomas algorithm (Thomas, 1995), the operational counts for solving an implicit two-level six-point scheme are less than double those for an explicit two-level four-point scheme.…”

Section: Order Of Accuracymentioning

confidence: 99%

Accuracy and Reliability Considerations of Option Pricing Algorithms

Kwok

Lau

2001

Journal of Futures Markets

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A wide variety of computational schemes have been proposed for the numerical valuation of various classes of options. Experiences in numerical computation have revealed that the details of the implementation of the auxiliary conditions in the numerical algorithms may have profound effects on numerical accuracy. Difficulties in designing algorithms that deal with the path-dependent payoffs, monitoring features, etc., have been well reported in the literature. In this article, the theoretical issues on the assessment of numerical schemes with regard to accuracy of approximation of auxiliary conditions, rate of convergence, and oscillation phenomena are reviewed. In particular, the oscillation phenomena in bond-price calculations and the intricacies in implementing the auxiliary conditions in barrier options, proportional step options, and lookback options are discussed. With different types of options and modes of monitoring (continuous or discrete), the optimal method of placing the lattice nodes with reference to

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“…The carrier wave functions and the subband energies are determined by numerically solving the Schrödinger equation and employing the finite difference method. 22 All the material parameters are taken from Ref. 23 for 300 K. The optical material gain of a quantum well, including a Lorentzian line-shape function, can be derived from Fermi's golden rule as…”

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confidence: 99%

Polarization-independent gain in mid-infrared interband cascade lasers

Ryczko

Sęk

2016

AIP Advances

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We have calculated the gain function of a type-II W-design AlSb/InAs/GaAsSb/InAs/AlSb quantum wells to be used in an active region of interband cascade lasers, for two linear polarizations of in-plane propagating light: transverse-electric and transverse-magnetic. The effect of external electric field, imitating the conditions in a working device, has also been taken into account. We have proposed an active region design suitable for practical realization of mid-infrared lasing devices with controllable polarization properties. We have also demonstrated a way to achieve polarization-independent gain in mid-infrared emitters, which has not been reported so far.

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Numerical Partial Differential Equations

Abstract: Library of Congress Cataloging-in-Publication Data Thomasj.W. Uames William), 1941-Numerical partial differential equations : finite difference methods I J.W. Thomas p. em. -(Texts in applied mathematics ; 22) Includes bibliographical references and index.

Cited by 166 publications

References 0 publications

Numerical validation of dispersion relations using a cylindrical wave for 2D FDTD methods

Numerical validation of dispersion relations using a cylindrical wave for 2D FDTD methods

Accuracy and Reliability Considerations of Option Pricing Algorithms

Polarization-independent gain in mid-infrared interband cascade lasers

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