Results 281 to 290 of about 491,048 (337)

Asymptotic behaviour and expansions of solutions of an ordinary differential equation

Russian Mathematical Surveys, 2004
Summary: An ordinary differential equation of quite general form is considered. It is shown how to find the following near a finite or infinite value of the independent variable by using algorithms of power geometry: (i) all power-law asymptotic expressions for solutions of the equation; (ii) all power-logarithmic expansions of solutions with power-law
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Application of Rational Expansion Method for Differential-Difference Equation

Communications in Theoretical Physics, 2011
In this paper, we applied the rational formal expansion method to construct a series of soliton-like and period-form solutions for nonlinear differential-difference equations. Compared with most existing methods, the proposed method not only recovers some known solutions, but also finds some new and more general solutions.
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On Convergent Series Expansions for Solutions of Nonlinear Ordinary Differential Equations

Doklady Mathematics, 2022
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Asymptotic expansions with exponential, power, and logarithmic functions for non-autonomous nonlinear differential equations

Journal of evolution equations (Printed ed.), 2019
This paper develops further and systematically the asymptotic expansion theory that was initiated by Foias and Saut in (Ann Inst H Poincaré Anal Non Linéaire, 4(1):1–47 1987).
Dat Cao, L. Hoang
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Exponential expansions of solutions to an ordinary differential equation

Doklady Mathematics, 2012
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Solving System of Fractional Differential Equations via Vieta-Lucas Operational Matrix Method

International Journal of Applied and Computational Mathematics, 2023
Rahul Chaudhary, Shivani Aeri, Anu Bala, Rakesh Kumar, D. Baleanu   +4 more
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APPLICATION OF SHOHAT EXPANSION IN PERIODIC SOLUTION OF DIFFERENTIAL EQUATIONS

Journal of Sound and Vibration, 1998
The failure of the Shohat expansion in the case of Duffing equation, can be attributed mainly to the hardening type of behaviour of the solution.
M.S. Sarma, B.Nageswara Rao
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Expansions Associated with a Pair of Singular First-Order Differential Equations

Journal of Mathematical Physics, 1963
This paper reports on the continuation of a study of the spectral properties of a Dirac operator. The analytical methods developed by Weyl and Titchmarsh for the analysis of the Sturm-Liouville equation are extended to the investigation of a system of two singular first-order differential equations. Expansions associated with the system are established
Roos, B. W., Sangren, W. C.
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Method of fast expansions for solving nonlinear differential equations

Computational Mathematics and Mathematical Physics, 2014
Summary: A method is proposed for constructing fast converging Fourier series with the help of a special boundary function \(M_q\). The convergence rate of the series is determined by the order \(q\) of \(M_q\), which makes it possible to use a small number of series terms.
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Chaos expansion for the solutions of stochastic differential equations

Systems & Control Letters, 1999
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