Stability of difference schemes for nonsymmetric linear hyperbolic systems with variable coefficients

Shintani, Hisayoshi; Tomoeda, Kenji

doi:10.32917/hmj/1206135965

Cited by 10 publications

(3 citation statements)

References 15 publications

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“…where k ε max the maximal norm of all wave vectors in the medium which can be estimated by ρ(ε)k max with k max being the maximal wave vector of the initial pulse in vacuum and ρ(ε) the maximal spectral radius of the symmetric matrix ε(x) over x (or simply the maximum of ε(x) if the medium is isotropic). This can be understood from the following principle [17]. A finite difference scheme with variable coefficients is stable if all the corresponding schemes with frozen (i.e., fixed to a particular value everywhere in space) coefficients are stable.…”

Section: A Modified Temporal Leapfrog Schemementioning

confidence: 99%

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Applications of the wave packet method to resonant transmission and reflection gratings

Borisov

Shabanov

2004

Journal of Computational Physics

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Scattering of femtosecond laser pulses on resonant transmission and reflection gratings made of dispersive (Drude metals) and dielectric materials is studied by a time-domain numerical algorithm for Maxwell's theory of linear passive (dispersive and absorbing) media. The algorithm is based on the Hamiltonian formalism in the framework of which Maxwell's equations for passive media are shown to be equivalent to the first-order equation, ∂Ψ/∂t = HΨ, where H is a linear differential operator (Hamiltonian) acting on a multi-dimensional vector Ψ built of the electromagnetic inductions and auxiliary matter fields describing the medium response. The initial value problem is then solved by means of a modified time leapfrog method in combination with the Fourier pseudospectral method applied on a non-uniform grid that is constructed by a change of variables and designed to enhance the sampling efficiency near medium interfaces. The algorithm is shown to be highly accurate at relatively low computational costs. An excellent agreement with previous theoretical and experimental studies of the gratings is demonstrated by numerical simulations using our algorithm. In addition, our algorithm allows one to see real time dynamics of long leaving resonant excitations of electromagnetic fields in the gratings in the entire frequency range of the initial wide band wave packet as well as formation of the reflected and transmitted wave fronts.

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Section: A Modified Temporal Leapfrog Schemementioning

confidence: 99%

“…Here the idea of the frozen coefficients [17] has been used again. The left hand side of inequality (5.16) is nothing but the spectral radius of ∆tH F 0 with frozen plasma frequencies so that ω p = ω max p .…”

Section: An Example Of the Lorentz Modelmentioning

confidence: 99%

Applications of the wave packet method to resonant transmission and reflection gratings

Borisov

Shabanov

2004

Journal of Computational Physics

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“…Typical examples are Friedrichs-Lax scheme and modified Lax-Wedroff scheme. (See Yamaguti and Nogi [6], Kametaka [9], Vaillancourt [8], Koshiba-Kumanogo [10], Sintani-Tomoeda [11], etc.) An A-stability theorem similar to Theorem 1.2 was given for a dissipative scheme of dissipative hermitian systems by B. Gustafsson [7].…”

Section: For All X and T;' A Smooth Diagonalizer î'(X T;') Or Symmementioning

confidence: 99%

Stability and A-stability of dissipative difference scheme for strongly hyperbolic systems

Nogi

2001

Japan J. Indust. Appl. Math.

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In this paper we give a stability theorem and an A-stability theorem of dissipative difference schemes for strongly hyperbolic systems with variable coefficients. The A-stability theorem is considered only in the case that those coefficients are differ from constant coefficients by sufficiently small variable parts. We prove them under the assumption that symbols of schemes have smooth symmetrizers, by using the theory of pseudo-difference operators.

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Stability of some difference schemes with C2-coefficients

Koshiba

1981

Journal of Mathematical Analysis and Applications

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Stability of difference schemes for nonsymmetric linear hyperbolic systems with variable coefficients

Cited by 10 publications

References 15 publications

Applications of the wave packet method to resonant transmission and reflection gratings

Applications of the wave packet method to resonant transmission and reflection gratings

Stability and A-stability of dissipative difference scheme for strongly hyperbolic systems

Stability of some difference schemes with C2-coefficients

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