Symmetry Lie algebras of nth order ordinary differential equations

Symmetries of nth-Order Approximate Stochastic Ordinary Differential Equations

Symmetries of nth-order approximate stochastic ordinary differential equations SODEs are studied. The determining equations of these SODEs are derived in an Itô calculus context. These determining equations are not stochastic in nature. SODEs are normally used tomodel nature e.g., earthquakes or for testing the safety and reliability of models in construction engineering when looking at the imp...

Application of the Lie Symmetry Analysis for second-order fractional differential equations

Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issue among mathematicians and engineers, specifically in recent years. The purpose of this paper Lie Symmetry method is developed to solve second-order fractional differential equations, based on conformable fractional derivative. Some numerical examples are presented to il...

Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations

A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equations subjected to some constraints and admitting a given Lie algebra as Vessiot-Guldberg-Lie algebr...

Order Ordinary Differential Equations

The DI methods for directly solving a system ofa general higher order ODEs are discussed. The convergence of the constant stepsize and constant order formulation of the DI methods is proven first before the convergencefor the variable order and stepsize case.

A Note on Four-Dimensional Symmetry Algebras and Fourth-Order Ordinary Differential Equations