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
Localized direct boundary–domain integro–differential formulations for scalar nonlinear boundary-value problems with variable coefficients [PDF]
, 2005 Mixed boundary-value Problems (BVPs) for a second-order quasi-linear elliptic partial differential equation with variable coefficients dependent on the unknown solution and its gradient are considered.
Mikhailov, SE
core +1 more source
On Linear Differential Equations Involving a Para-Grassmann Variable [PDF]
, 2009 As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly.
Mansour, Toufik, Schork, Matthias
core +5 more sources
Differential Equations for Algebraic Functions [PDF]
, 2007 It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions.
Bostan, Alin +4 more
core +9 more sources
On the use of Hadamard expansions in hyperasymptotic evaluation: differential equations of hypergeometric type [PDF]
, 2004 We describe how a modification of a common technique for developing asymptotic expansions of solutions of linear differential equations can be used to derive Hadamard expansions of solutions of differential equations.
Kaminski, D., Paris, Richard B.
core +3 more sources
Linear differential equations for families of polynomials
Journal of Inequalities and Applications, 2016 In this paper, we present linear differential equations for the generating functions of the Poisson-Charlier, actuarial, and Meixner polynomials. Also, we give an application for each case.
Taekyun Kim +3 more
doaj +1 more source
The Z5 transformation for solving quasi-linear partial differential equations
Partial Differential Equations in Applied Mathematics, 2023 The Z1-Z4 transformations proposed in our previous papers have acquired remarkable success in the field of linear partial differential equations, general solutions of a large number of typical equations were obtained for the first time, and exact ...
Hong Lai Zhu
doaj +1 more source
A Problem in Linear Differential Equations [PDF]
Proceedings of the American Mathematical Society, 1959 In the Bulletin of the American Mathematical Society, March 1958, page 61, R. E. Bellman suggests the following for research. "Consider the second order linear differential equation (1) u" + (1 + Xg(x))u = O where X is a real constant and fo7 I g(x) I dx 0 for x _ 0, is the singularity nearest the origin on the negative axis?" We assume that g(x) is ...
openaire +1 more source
Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlev\'e VI [PDF]
, 2018 We investigate the recurrence coefficients of discrete orthogonal polynomials on the non-negative integers with hypergeometric weights and show that they satisfy a system of non-linear difference equations and a non-linear second order differential ...
Filipuk, Galina, Van Assche, Walter
core +3 more sources
General Solution of Linear Fractional Neutral Differential Difference Equations
Discrete Dynamics in Nature and Society, 2013 This paper is concerned with the general solution of linear fractional neutral differential difference equations. The exponential estimates of the solution and the variation of constant formula for linear fractional neutral differential difference ...
Hai Zhang, Jinde Cao, Wei Jiang
doaj +1 more source