Extended rational expansion method for differential-difference equation
Applied Mathematics and Computation, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Magnus Expansion for Periodic Delay Differential Equations
Volume 7B: 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, 2013In this paper, the application of the Magnus expansion on periodic time-delayed differential equations is proposed, where an approximation technique of Chebyshev Spectral Continuous Time Approximation (CSCTA) is first used to convert a system of delayed differential equations (DDEs) into a system of ordinary differential equations (ODEs), whose ...
Árpád Takács +2 more
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Pole expansions of nonlinear partial differential equations
Il Nuovo Cimento B Series 11, 1977Pole 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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Factored Product Expansions of Solutions of Nonlinear Differential Equations
SIAM Journal on Mathematical Analysis, 1984Lie 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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Asymptotic behaviour and expansions of solutions of an ordinary differential equation
Russian Mathematical Surveys, 2004Summary: 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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Asymptotic Expansions for the Midpoint Rule Applied to Delay Differential Equations
SIAM Journal on Numerical Analysis, 1986zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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EXPANSIONS IN EIGENFUNCTIONS OF A TWO-PARAMETER SYSTEM OF DIFFERENTIAL EQUATIONS
Quaestiones Mathematicae, 1986Abstract Techniques from the theory of partial differential equations are used to prove the uniform convergence of the eigenfunction expansion associated with a two-parameter system of ordinary differential equations of the second order under left definiteness and semi-definitness assumptions.
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Expansive functions and quasilinear Jacobi differential equations
Nonlinear Analysis: Theory, Methods & Applications, 1994The sufficient and necessary conditions for weak solvability of a Jacobi type quasilinear differential equation are deduced.
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High order one-step methods for backward stochastic differential equations via Itô-Taylor expansion
Discrete and Continuous Dynamical Systems - Series B, 2022Yabing Sun
exaly
EIGENFUNCTION EXPANSIONS ASSOCIATED WITH PARTIAL DIFFERENTIAL EQUATIONS
The Quarterly Journal of Mathematics, 1966openaire +1 more source