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Periodic Solutions and Approximate Symmetries
Nonlinear Dynamics, 2000This paper deals with the geometrical approach to study the approximate symmetries of the approximate dynamical system obtained in the neighborhood of a periodic solution. The author demonstrates own results on the damped-driven Helmholtz oscillator which arises in modeling of ear drums and ship capsizing.
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Periodic Solutions by Picard's Approximations
Canadian Mathematical Bulletin, 1968In [1] Demidovic considered a system of linear differential equationswith A(t) continuous, T-periodic, odd, and skew symmetric. He proved that all solutions of (1) are either T-periodic or 2T-periodic0 In [2] Epstein used Floquet theory to prove that all solutions of (1) are T-periodic without the skew symmetric hypothesis.
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Recursive Best Approximate Solution Algorithms
SIAM Journal on Algebraic Discrete Methods, 1985System identification based on the least square approach is studied. Recursive algorithms for computing the best approximate solution to the linear multivariate sequential estimation problem are developed. The approach is based on an application of the matrix pseudoinversion lemma, which was proved by the author [ibid. 6, 371-377 (1985; Zbl 0573.15003)]
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Approximate Solution of Hill's Equation
Journal of Mathematical Physics, 1966A modified WKB approximation, amenable to successive corrections, to the solution of the linear differential equation of second order having a periodic coefficient in normal form is presented. Considered as an application of the related equation method, it uses the free-particle wave equation rather than, as in an alternative approach, Mathieu's ...
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Global optimal approximate solutions
Optimization Letters, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Solution of Approximate Equations
1986In this chapter we wish to explore some of the ideas surrounding approximate equations. The basic idea is the following: if we are confronted with a nonlinear differential equation whose solution is unknown, then we would like to replace this equation with a set, one or more, of approximating equations whose solutions are known.
Richard E. Bellman, Robert S. Roth
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
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