Stability and dynamical properties of Rosenau-Hyman compactons using Padé approximants
نویسندگان
چکیده
منابع مشابه
Stability and dynamical properties of Rosenau-Hyman compactons using Padé approximants.
We present a systematic approach for calculating higher-order derivatives of smooth functions on a uniform grid using Padé approximants. We illustrate our findings by deriving higher-order approximations using traditional second-order finite-difference formulas as our starting point. We employ these schemes to study the stability and dynamical properties of K(2,2) Rosenau-Hyman compactons inclu...
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The numerical simulation of compactons, solitary waves with compact support, is characterized by the presence of spurious phenomena, as numerically-induced radiation, which is illustrated here using four numerical methods applied to the RosenauHyman K(p, p) equation. Both forward and backward radiations are emitted from the compacton presenting a self-similar shape which has been illustrated gr...
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Extending a Padé approximant method used for studying compactons in the Rosenau-Hyman (RH) equation, we study the numerical stability of single compactons of the Cooper-Shepard-Sodano (CSS) equation and their pairwise interactions. The CSS equation has a conserved Hamiltonian which has allowed various approaches for studying analytically the nonlinear stability of the solutions. We study three ...
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For a recent new numerical method for computing so-called robust Padé approximants through SVD techniques, the authors gave numerical evidence that such approximants are insensitive to perturbations in the data, and do not have so-called spurious poles, that is, poles with a close-by zero or poles with small residuals. A black box procedure for eliminating spurious poles would have a major impa...
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Let µ be a finite positive Borel measure whose support is a compact subset K of the real line and let I be the convex hull of K. Let r denote a rational function with real coefficients whose poles lie in C \ I and r(∞) = 0. We consider multipoint rational interpolants of the function f (z) = dµ(x) z − x + r(z), where some poles are fixed and others are left free. We show that if the interpolati...
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2010
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.81.056708