Results 31 to 40 of about 290,072 (190)

Integrability of Stochastic Birth-Death processes via Differential Galois Theory [PDF]

, 2019
Stochastic birth-death processes are described as continuous-time Markov processes in models of population dynamics. A system of infinite, coupled ordinary differential equations (the so-called master equation) describes the time-dependence of the ...
Acosta-Humanez, Primitivo B., Capitan, Jose A., Morales-Ruiz, Juan J.   +2 more
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Physical applications of second-order linear differential equations that admit polynomial solutions

, 2010
Conditions are given for the second-order linear differential equation P3 y" + P2 y'- P1 y = 0 to have polynomial solutions, where Pn is a polynomial of degree n. Several application of these results to Schroedinger's equation are discussed.
Ciftci H, Ebubekir Dogu, Fiziev P P, Fryantsev A V, Hakan Ciftci, Krall H L, Krylov G, Krylov G, Littlejohn L L, Lyskova A S, Nasser Saad, Nikiforov A F, Ray P P, Richard L Hall, Ronveaux A, Saad N, Slavyanov S Y   +16 more
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Functional Relations in Stokes Multipliers and Solvable Models related to U_q(A^{(1)}_n) [PDF]

, 2000
Recently, Dorey and Tateo have investigated functional relations among Stokes multipliers for a Schr{\"o}dinger equation (second order differential equation) with a polynomial potential term in view of solvable models.
Baxter R J, Bazhanov V V, Bazhanov V V, Bazhanov V V, Cherednik I, Date E, Dorey P, Dorey P, Dorey P, Dorey P, Fedoryuk M V, Feigin B, Fendley P, Hsieh P-F, J Suzuki, Jüttner G, Kawai T, Kirillov A N, Klümper A, Klümper A, Kuniba A, Kuniba A, Kuniba A, Macdonald I G, Olde Daalhuis A B, Scheffé H, Shibuya Y, Sklyanin E, Suzuki J, Suzuki J, Suzuki J, Suzuki J, Suzuki J, Trjitzinsky W J, Turrittin H L, Voros A, Voros A, Voros A, Voros A, Voros A, Voros A, Voros A   +41 more
core   +2 more sources

Polynomial Differential Equations with Piecewise Linear Coefficients [PDF]

Differential Equations and Dynamical Systems, 2011
Cubic and quartic non-autonomous differential equations with continuous piecewise linear coefficients are considered. The main concern is to find the maximum possible multiplicity of periodic solutions. For many classes, we show that the mutiplicity is the same when the coefficients are polynomial functions of degree n or piecewise linear functions ...
openaire   +2 more sources

Combination of integral and projected differential transform methods for time-fractional gas dynamics equations

Ain Shams Engineering Journal, 2018
The present paper discusses the solution of nonlinear homogeneous and nonhomogeneous time-fractional gas dynamic equations arising in shock fronts by a new combination of new integral and projected differential transform method.
Kunjan Shah, Twinkle Singh, Adem Kılıçman   +2 more
doaj   +1 more source

On polynomial solutions of Heun equation

, 2004
By making use of a recently developed method to solve linear differential equations of arbitrary order, we find a wide class of polynomial solutions to the Heun equation.
Bhaduri R K, Christ N H, Dorey P, Gradshteyn I S, Gurappa N, Maier R S, N Gurappa, Prasanta K Panigrahi, Ronveaux A, Suzuki M, Takemura K   +10 more
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Tropical differential equations [PDF]

, 2015
Tropical differential equations are introduced and an algorithm is designed which tests solvability of a system of tropical linear differential equations within the complexity polynomial in the size of the system and in its coefficients.
Grigoriev, Dima
core   +1 more source

Orthogonal Polynomials and Second-order Differential Equations [PDF]

IMA Journal of Applied Mathematics, 1983
\textit{S. Bochner} [Math. Z. 29, 730-736 (1929)] showed that a sequence of polynomials \(\{p_ n(x)\}\) with \(p_ n(x)\) of precise degree n, satisfies a differential equation of the form \[ (*)\quad a_ 0(x)y''\!_ n+a_ 1(x)y'\!_ n+a_ 2(x)y_ n=\lambda_ ny_ n \] only in a very limited set of cases corresponding essentially to the ''classical'' orthogonal
openaire   +3 more sources

Numerical method for a system of integro-differential equations and convergence analysis by Taylor collocation

Ain Shams Engineering Journal, 2018
In this paper, we present the Taylor polynomial solutions of system of higher order linear integro-differential Volterra-Fredholm equations (IDVFE). This method transforms IDVFE into the matrix equations which correspond to a system of linear algebraic ...
Yousef Jafarzadeh, Bagher Keramati
doaj   +1 more source

Exact single traveling wave solutions to generalized (2+1)-dimensional Gardner equation with variable coefficients

Results in Physics, 2019
We firstly apply the trial equation method to generalized (2+1)-dimensional Gardner equation to reduce the nonlinear partial differential equation into ordinary equation.
Yue Kai, Bailin Zheng, Nan Yang, Wenlong Xu   +3 more
doaj   +1 more source