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  1. Computational Mathematics and Mathematical Physics
  2. Computational Mathematics and Mathematical Physics : Volume 48
  3. Computational Mathematics and Mathematical Physics : Volume 48, Issue 4, April 2008
  4. Cauchy problem for Mathieu’s equation at parametric resonance
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Computational Mathematics and Mathematical Physics : Volume 57
Computational Mathematics and Mathematical Physics : Volume 56
Computational Mathematics and Mathematical Physics : Volume 55
Computational Mathematics and Mathematical Physics : Volume 54
Computational Mathematics and Mathematical Physics : Volume 53
Computational Mathematics and Mathematical Physics : Volume 52
Computational Mathematics and Mathematical Physics : Volume 51
Computational Mathematics and Mathematical Physics : Volume 50
Computational Mathematics and Mathematical Physics : Volume 49
Computational Mathematics and Mathematical Physics : Volume 48
Computational Mathematics and Mathematical Physics : Volume 48, Issue 12, December 2008
Computational Mathematics and Mathematical Physics : Volume 48, Issue 11, November 2008
Computational Mathematics and Mathematical Physics : Volume 48, Issue 10, October 2008
Computational Mathematics and Mathematical Physics : Volume 48, Issue 9, September 2008
Computational Mathematics and Mathematical Physics : Volume 48, Issue 8, August 2008
Computational Mathematics and Mathematical Physics : Volume 48, Issue 7, July 2008
Computational Mathematics and Mathematical Physics : Volume 48, Issue 6, June 2008
Computational Mathematics and Mathematical Physics : Volume 48, Issue 5, May 2008
Computational Mathematics and Mathematical Physics : Volume 48, Issue 4, April 2008
Iterative processes based on block H-splittings
Linear interval equations with symmetric solution sets
Construction of hyperbolic interpolation splines
Computational scheme for invariantly unbiased estimation of linear operators in a given class
Decentralized optimal control of a group of dynamical objects
Method of orthogonal simplexes and its applications to convex programming
Optimal control of a magnetohydrodynamic viscous heat-conducting gas flow
Cauchy problem for Mathieu’s equation at parametric resonance
On certain alternating boundary-layer solutions to singularly perturbed parabolic equations
Approximation of a system of singularly perturbed reaction-diffusion parabolic equations in a rectangle
Reconstruction of the right-hand side of a parabolic equation
Analytical solutions to the heat conduction problems for a cylinder and a ball based on determining the temperature perturbation front
Fronts, traveling fronts, and their stability in the generalized Swift-Hohenberg equation
Iterative method for finding the eigenfunctions of a system of two Schrödinger equations with combined nonlinearity
Influence of cubic nonlinearity on the dispersion relation for long waves on a water surface
Computational Mathematics and Mathematical Physics : Volume 48, Issue 3, March 2008
Computational Mathematics and Mathematical Physics : Volume 48, Issue 2, February 2008
Computational Mathematics and Mathematical Physics : Volume 48, Issue 1, January 2008
Computational Mathematics and Mathematical Physics : Volume 47
Computational Mathematics and Mathematical Physics : Volume 46

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Cauchy problem for Mathieu’s equation at parametric resonance

Content Provider Springer Nature Link
Author Kurin, A. F.
Copyright Year 2008
Abstract Mathieu’s equation is solved by an asymptotic averaging method in the fourth approximation for the first to fourth resonance domains and in the third approximation for the zero resonance domain. The general periodic and aperiodic solutions on characteristic curves are found, and the general solution is obtained in instability domains and stability-domain areas adjacent to the characteristic curves. All the solutions are explicitly found in the form of functions of an argument without using the auxiliary parameter employed in Whittaker’s method. Simple formulas depending on two parameters of the equation are derived for the characteristic exponent in instability domains and for the frequency of slow oscillations in stability domains near the characteristic curves. The theory is developed by analyzing the resonances exhibited by Mathieu’s equation.
Starting Page 600
Ending Page 617
Page Count 18
File Format PDF
ISSN 09655425
Journal Computational Mathematics and Mathematical Physics
Volume Number 48
Issue Number 4
e-ISSN 15556662
Language English
Publisher SP MAIK Nauka/Interperiodica
Publisher Date 2008-05-07
Publisher Place Dordrecht
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Cauchy problem Mathieu’s equation averaging method resonance stability Computational Mathematics and Numerical Analysis
Content Type Text
Resource Type Article
Subject Computational Mathematics
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