Results 291 to 300 of about 491,048 (337)

Adiabatic expansions of solutions of coupled second−order linear differential equations. I

Journal of Mathematical Physics, 1975
A generalized higher−order WKB approximation is found for the set of equations h″j(t) + u2 𝒥Nk=1 Mjk(t)hk(t) = 0 (u → ∞), when the coefficients Mjk form a positive definite Hermitian matrix M satisfying a smoothness condition as a function of t. In the construction, essential use is made of a transformation introduced by Kato to connect smoothly the ...
openaire   +1 more source

EXPANSIONS IN EIGENFUNCTIONS OF A TWO-PARAMETER SYSTEM OF DIFFERENTIAL EQUATIONS

Quaestiones Mathematicae, 1986
Abstract 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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Dispersion analysis and improved F-expansion method for space–time fractional differential equations

Nonlinear dynamics, 2019
B. Kaur, R. Gupta
semanticscholar   +1 more source

The Magnus Expansion for Stochastic Differential Equations

Journal of nonlinear science, 2019
Zhenyu Wang, Q. Ma, Zhen Yao, X. Ding
semanticscholar   +1 more source

Itô–Taylor Expansions for Systems of Stochastic Differential Equations with Applications to Stochastic Partial Differential Equations

2017
Stochastic differential equations (SDEs) are playing a growing role in financial mathematics, actuarial sciences, physics, biology and engineering. For example, in financial mathematics, fluctuating stock prices and option prices can be modeled by SDEs.
Fikriye Yılmaz, Hacer Öz Bakan, Gerhard-Wilhelm Weber   +2 more
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Stochastic integration and differential equations

, 1990
P. Protter
semanticscholar   +1 more source

A novel expansion iterative method for solving linear partial differential equations of fractional order

Applied Mathematics and Computation, 2015
Ahmad El-Ajou, O. A. Arqub, S. Momani, D. Baleanu, A. Alsaedi   +4 more
semanticscholar   +1 more source

Solving integral equations in free space with inverse-designed ultrathin optical metagratings

Nature Nanotechnology, 2023
Andrea Cordaro, Andrea Alu
exaly  

DeepXDE: A Deep Learning Library for Solving Differential Equations

SIAM Review, 2021
Lu Lu, George E Karniadakis
exaly  

Some general problems of the theory of ordinary linear differential equations and expansion of an arbitrary function in series of fundamental functions

, 1928
J. Tamarkin
semanticscholar   +1 more source