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1.
The homotopic mapping method for sea-air oscillator model of interdecadal climate fluctuations 总被引:2,自引:0,他引:2
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The E1 Nifio/La Nifia Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, a coupled system of sea-air oscillator model is studied. The aim is to create an asymptotic solving method of nonlinear equation for the ENSO model. And based on a class of oscillators of ENSO model, employing the method of homotopic mapping, the approximate solution of corresponding problem is studied. It is proven from the results that the homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for ENSO model. 相似文献
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The periodic solution to a delayed sea-air oscillator coupling model for the El Nifio-Southern Oscillation (ENSO)
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A time-delay sea-air oscillator coupling model is studied. Using Mawhin's continuation theorem, the result on the existence of periodic solutions for the sea-air oscillator model is obtained. 相似文献
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A time delay equation for the sea--air oscillator model is studied. The aim is to
create an asymptotic solving method of nonlinear equation for the El Ni\tilde{\rm
n}o--Southern Oscillation model. And based on a class of oscillators of the
model, employing the method of ENSO singular perturbation, the asymptotic solution
of corresponding problem is obtained. It is proven from the results that the method
of singular perturbation can be used for analysing the sea surface temperature
anomaly in the equatorial eastern Pacific of the atmosphere--ocean oscillation for
ENSO model. 相似文献
4.
Existence and asymptotic estimates of periodic solutions of a sea--air oscillator model of decadal variations in subtropical cells and equatorial Pacific SST
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This paper studies a time delay equation for sea-air oscillator model. The existence and asymptotic estimates of periodic solutions of corresponding problem are obtained by employing the technique of upper and lower solution, and by using the continuation theorem of coincidence degree theory. 相似文献
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Perturbation method of studying the EI Nifio oscillation with two parameters by using the delay sea-air oscillator model
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The EI Nio-southern oscillation (ENSO) is an interannual phenomenon involved in tropical Pacific oceanatmosphere interactions. In this paper, we develop an asymptotic method of solving the nonlinear equation using the ENSO model. Based on a class of the oscillator of the ENSO model, a approximate solution of the corresponding problem is studied employing the perturbation method. 相似文献
10.
Perturbation method of studying the EI Niño oscillation with two parameters using delay sea—air oscillator model
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The EI Niño-southern oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, we develop an asymptotic method of solving the nonlinear equation using the ENSO model. Based on a class of oscillator of the ENSO model, a approximate solution of the corresponding problem is studied employing the perturbation method. 相似文献
11.
Homotopic method of solving a class of EI Nino/La Nina-Southern Oscillation sea-air oscillator
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The EI Nino/La Nina-Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific Ocean-atmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is created. And based on a class of oscillator of the ENSO model, the approximate solution of a corresponding problem is studied by employing the method of homotopic mapping. It is proved from the results that the homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for the ENSO model. 相似文献
12.
The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the ‘cubication’ of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used. 相似文献
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The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to an oscillating charge in the electric field of a ring. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed. 相似文献
14.
Asymptotic solution for a class of sea-air oscillator model for El Nin^~o-southern oscillation
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The El Nifio-Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is used. And based on a class of oscillator of ENSO model, the approximate solution of a corresponding problem is studied by employing the perturbation method. Firstly, an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced, Secondly, by using the perturbed method, the zeroth and first order asymptotic perturbed solutions are constructed. Finally, from the comparison of the values for a figure, it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy. And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model. 相似文献
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采用改进的L-P法研究一维相对率振子动方程的近似解,此法克服了参数摄动法易出现长期项,而建立补充方程和须解微分方程的弊病。 相似文献
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The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency-amplitude relations for the relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Making a change of variable, a new nonlinear differential equation is obtained and two procedures are used to approximately solve this differential equation. In the first the differential equation is rewritten in a form that does not contain a square-root expression, while in the second the differential equation is solved directly. The approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first due to the fact that, in the second procedure, application of the harmonic balance method produces an infinite set of harmonics, while in the first procedure only two harmonics are produced. Both approximate frequencies are valid for the complete range of oscillation amplitudes, and excellent agreement of the approximate frequencies with the exact one are demonstrated and discussed. The discrepancy between the first-order approximate frequency obtained by means of the second procedure and the exact frequency never exceeds 1.6%. We also obtained the approximate frequency by applying the second-order harmonic balance method and in this case the relative error is as low 0.31% for all the range of values of amplitude of oscillation A. 相似文献
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Exact and Approximate Values of the Period for a "Truly Nonlinear" Oscillator: $\ddot{x} + x + x^{1/3} = 0$
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Ronald E. Mickens & Dorian Wilkerson 《advances in applied mathematics and mechanics.》2009,1(3):383-390
We investigate the mathematical properties of a "truly nonlinear" oscillator
differential equation. In particular, using phase-space methods, it is shown
that all solutions are periodic and the fixed-point is a nonlinear center. We calculate
both exact and approximate analytical expressions for the period, where the exact
solution is given in terms of elliptic functions and the method of harmonic balance
is used to calculate the approximate formula. 相似文献
20.
We sketch the integral variation method for generating approximate solutions to initial value problems involving systems of first-order ordinary differential equations. This new constructive technique is illustrated with applications to the damped oscillator, a nonlinear growth equation, and zonal harmonic perturbations of a near Earth satellite orbit. 相似文献