Results 271 to 280 of about 491,048 (337)

Pole expansions of nonlinear partial differential equations

Il Nuovo Cimento B Series 11, 1977
Pole expansions of certain solutions of various nonlinear partial differential equations are investigated. The most interesting results obtain for the Korteweg-de Vries and especially for the Burgers-Hopf equations. The motion of the poles is shown to correspond formally to the motion of one-dimensional particles interacting via simple two-body ...
D. V. Choodnovsky, G. V. Choodnovsky
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Taylor series expansion of delay differential equations—A warning

Journal of Theoretical Biology, 1974
Abstract Attempts have been made to approximate the solutions of differential-difference equations using a Taylor series expansion of the lag term and ignoring high order derivatives. It is demonstrated that such a technique may lead to serious errors and that it is, perhaps, easier and certainly more valid to apply numerical methods directly.
A, Mazanov, K P, Tognetti
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Expansions of Differential Operators and Nonsmooth Solutions of Differential Equations

Cybernetics and Systems Analysis, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Series Expansions of Solutions of Differential-Difference Parabolic Equations

Mathematical Notes
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Muravnik, A. B., Yaremko, O. É., Yaremko, N. N.   +2 more
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Asymptotic Expansions of Solutions of Differential Equations

Journal of Mathematical Physics, 1965
A generalization of Ford's method, concerning the asymptotic expansions of solutions of differential equations with polynomial coefficients and with three or more regular singular points and one irregular at infinity, is presented. The analysis is subsequently extended to the special case of integral values for the difference of exponents of the ...
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Factored Product Expansions of Solutions of Nonlinear Differential Equations

SIAM Journal on Mathematical Analysis, 1984
Lie transformations are used to represent solutions of initial value problems for systems of nonlinear ordinary differential equations as exponentials of first order linear partial differential operators. These exponentials are then expanded using an analog of the usual exponential identities.
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Sixth-Kind Chebyshev Spectral Approach for Solving Fractional Differential Equations

International journal of nonlinear sciences and numerical simulation, 2019
The basic aim of this paper is to develop new numerical algorithms for solving some linear and nonlinear fractional-order differential equations. We have developed a new type of Chebyshev polynomials, namely, Chebyshev polynomials of sixth kind.
W. Abd-Elhameed, Youssri Hassan Youssri
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Application of rational expansion method for stochastic differential equations

Applied Mathematics and Computation, 2012
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Wang, Meijiao, Wang, Qi
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All-order differential equations for one-loop closed-string integrals and modular graph forms

Journal of High Energy Physics, 2019
We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and type-II theories.
Jan E. Gerken, A. Kleinschmidt, O. Schlotterer   +2 more
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On certain expansions of the solutions of Mathieu'S differential equation

Mathematical Proceedings of the Cambridge Philosophical Society, 1942
1. There are several known types of expansions of Mathieu functions, i.e. mod 2π periodic solutions of Mathieu's equation ((9), chap. 19),The simplest expansion is the Fourier seriesAlmost equally well known are Heine's expansion ((4), p.
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