Related papers: Reduction of fourth order ordinary differential eq…
Our paper "Solving Third Order Linear Difference Equations in Terms of Second Order Equations" gave two algorithms for solving difference equations in terms of lower order equations: an algorithm for absolute factorization, and an algorithm…
A characterization of the symmetry algebra of the $n$th order ordinary differential equations (ODEs) with maximal symmetry and all third order linearizable ODEs is given. This is used to show that such an algebra $\mathfrak{g}$ determines…
Linearization problem of ordinary differential equations by a new set of tangent transformations is considered in the paper. This set of transformations allows one to extend the set of transformations applied for the linearization problem.…
A full Lie analysis of a system of third-order difference equations is performed. Explicit solutions, expressed in terms of the initial values, are derived. Furthermore, we give sufficient conditions for existence of 2-periodic and…
In this paper we show how to find a closed form solution for third order difference operators in terms of solutions of second order operators. This work is an extension of previous results on finding closed form solutions of recurrence…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
We derive a method for finding Lie Symmetries for third-order difference equations. We use these symmetries to reduce the order of the difference equations and hence obtain the solutions of some third-order difference equations. We also…
Invariant linearization criteria of square systems of second-order quadratically semi-linear ordinary differential equations (ODEs) that can be represented as geodesic equations are extended to square systems of ODEs cubically nonlinear in…
This paper is centred on solving differential equations by symmetry groups for first order ODEs and is in response to Starrett (2007). It also explores the possibility of averting the assumptions by Olver (2000) that, in practice finding…
This paper discusses model order reduction of large sparse second-order index-3 differential algebraic equations (DAEs) by applying Iterative Rational Krylov Algorithm (IRKA). In general, such DAEs arise in constraint mechanics, multibody…
The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…
The Lagrangian formalism for variational problem for second-order delay ordinary differential equations (DODEs) is developed. The Noether-type operator identities and theorems for DODEs of second order are presented. Algebraic construction…
For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a…
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…
The article proposes an approach to complete-type and related Lyapunov-Krasovskii functionals that neither requires knowledge of the delay-Lyapunov matrix function nor does it involve linear matrix inequalities. The approach is based on…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
Delay differential equations (DDEs) are infinite-dimensional systems, so even a scalar, unforced nonlinear DDE can exhibit chaos. Lyapunov exponents are indicators of chaos and can be computed by comparing the evolution of infinitesimally…
We propose a novel quantum algorithm for solving linear autonomous ordinary differential equations (ODEs) using the Pad\'e approximation. For linear autonomous ODEs, the discretized solution can be represented by a product of matrix…
We study second order and third order linear differential equations with analytic coefficients under the viewpoint of finding formal solutions and studying their convergence. We address some untouched aspects of Frobenius methods for second…
In this paper, we introduce some analytical techniques to solve some classes of second order differential equations. Such classes of differential equations arise in describing some mathematical problems in Physics and Engineering.