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  • 1
    Electronic Resource
    Electronic Resource
    A new family of Runge–Kutta type methods for the numerical integration of perturbed oscillators (1999)
    Springer
    Numerische Mathematik 82 (1999), S. 635-646 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65L05, 65L06
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. Our task in this paper is to present a new family of methods of the Runge–Kutta type for the numerical integration of perturbed oscillators. The key property is that those algorithms are able to integrate exactly, without truncation error, harmonic oscillators, and that, for perturbed problems the local error contains the perturbation parameter as a factor. Some numerical examples show the excellent behaviour when they compete with Runge–Kutta–Nyström type methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050434
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  • 2
    Electronic Resource
    Electronic Resource
    Two-point quasifractional approximant in physics. Truncation error (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1470-1477 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The quasifractional approximation method is developed in a systematic manner. This method uses simultaneously the power series, and at a second point, the asymptotic expansion. The usual form of the approximants is two or more rational fractions, in terms of a suitable variable, combined with auxiliary nonfractional functions. Coincidence in the singularities in the region of interest is pursued. Equal denominators in the rational fractions is required so that the solution of only linear algebraic equations is needed to determine the parameters of the approximant. An upper bound is obtained for the truncation error for a certain class of functions, which contains most of the functions for which this method has been applied so far. It is shown that quasifractional approximants can be derived as a mixed German and Latin polynomial problem in the context of Hermite–Padé approximation theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529304
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  • 3
    Electronic Resource
    Electronic Resource
    Experimental verification of the grid effects in a velocity analyzer with variable geometry (1986)
    [S.l.] : American Institute of Physics (AIP)
    Review of Scientific Instruments 57 (1986), S. 1507-1511 
    Details
    ISSN: 1089-7623
    Source: AIP Digital Archive
    Topics: Physics , Electrical Engineering, Measurement and Control Technology
    Notes: A velocity analyzer with adjustable interelectrodic distances is described here. Several experiments have been performed in a double plasma machine with this analyzer of variable geometry in order to investigate the effects of the discontinuous structure of the grids. The measured displacements of the characteristic curve for different interelectrodic distances show excellent agreement with the theoretical predictions due to the depletion of the discriminating potential in the holes of the grid, as is shown in our recent theoretical analysis using a Schwarz–Christoffel transformation. The influence of the grid structure on the temperature determined from the characteristic curve is also investigated and the correlation experiment theory is qualitatively correct.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1138576
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  • 4
    Electronic Resource
    Electronic Resource
    Improved solutions to the nonlinear one-dimensional Debye screening in plasmas with two temperatures (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 2105-2109 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Three new approximants to the solution of the one-dimensional nonlinear Debye screening potential have been obtained. The ions and electrons are in steady-state equilibrium situations with different temperatures. Therefore, the potential satisfies the nonlinear Poisson equation with a Boltzmann factor for both the electronic and ion densities. To obtain the approximants, the original equation has been written in a suitable compact way. The variables have been transformed in such a way that the two-point quasifractional approximation technique can be applied. The simplest approximant is almost as simple as the usual linear one, but it has an additional coefficient and it is more accurate. The other two approximants, more accurate than the simplest one, are exact for the limit of equal temperatures. All the approximants obtained here give better accuracy than the third-order approximation obtained previously by Clemente and Martín [J. Phys. Soc. Jpn. 61, 34 (1992)].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870607
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  • 5
    Electronic Resource
    Electronic Resource
    Fractional approximation to elliptic functions (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 330-333 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Jacobi functions sn(x/m) have been approximated by a quotient of polynomials of first to fourth degrees. The method used here is an extension to nonlinear differential equations of one previously published for first- and second-order linear differential equations. That method uses power series and asymptotic expansions simultaneously. The accuracy here obtained is very good (the absolute error is lower than 10−8 for m〈0.8) except for values of the parameter m near 1. They are much better for several orders of magnitude than those based on the Padé method for the same number of parameters to be determined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527661
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  • 6
    Electronic Resource
    Electronic Resource
    Fractional approximations to the Bessel function J0(x) (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 705-707 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A method to obtain fractional approximations to the Bessel function J0(x) is reported here. This method improves a recently published one principally in that all the parameters are uniquely determined by linear equations. Our approximations give fairly good accuracy for all real, positive values. The maximum absolute error for the first-degree approximation is about 0.0035, and for the fourth-degree one, about 2.8×10−6.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526610
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  • 7
    Electronic Resource
    Electronic Resource
    Ion-acoustic dispersion relation with direct fractional approximation for Z′(s) (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1186-1188 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A direct fractional approximation for the derivative Z′ of the plasma dispersion function Z(s) has been obtained by using the modified asymptotic Padé method. The dispersion relation for the ion-acoustic wave and for the ion-beam instability has been solved by the use of that fractional approximation yielding satisfactory results. A comparison is given between the dispersion relations calculated with (a) our approximation, (b) other approximations to Z′, and (c) the exact function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526523
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  • 8
    Electronic Resource
    Electronic Resource
    Fractional approximation to the vacuum–vacuum amplitude of a φ4-potential theory in zero dimensions (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 699-702 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Here, the vacuum–vacuum amplitude with a φ4-potential in terms of the fractional approximation to the partition function of a zero-dimensional field theory is presented. This fractional approximation has been obtained from both the power series and the asymptotic expansion. The power series diverges, nonetheless the fractional approximations are excellent. All the approximations from first to seventh degree are presented, with maximum errors from 0.6% to 1.6×10−5%, respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527172
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  • 9
    Electronic Resource
    Electronic Resource
    New first-order perpendicular drift velocities (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 1041-1044 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A treatment in orbit theory has been performed assuming that the parallel electric field E(parallel) and E⊥ are of zeroth order in m/q, i.e., they are O(1). A proper analysis is developed in such a way that no secularities appear. New first-order drift velocities have been found which depend on E(parallel).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.860950
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  • 10
    Electronic Resource
    Electronic Resource
    Gyroinvariant high-order orbit theory for unidirectional magnetostatic fields: New approach (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 11-21 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Gyroinvariant drift velocities and first adiabatic invariants have been determined in a unidirectional magnetic field B=B(x,y)bˆ, to fourth and third order of accuracy, respectively. The new method described here uses nonanalytical complex functions and successive integration by parts, combined with a suitable average over a quasiperiodic function. A suitable definition of the guiding center to any order is discussed and its position determined to fourth order of accuracy. A non-Hamiltonian method is described to find the first adiabatic invariant.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.859522
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