In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry method for third-order differential equations.In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry m...

in this paper, a numerical solution for a system of linear fredholm integro-differential equations by means of the sinc method is considered. this approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. the exponential convergence rate $o(e^{-k sqrt{n}})$ of the method is proved. the analytical results are illustrated with numerical examp...

in this paper, we consider non-linear ginsburg-pitaevski-gross equation with the rosen-morse and modifiedwoods-saxon potentials which is corresponding to the quantum vortices and has important applications in turbulence theory. we use the runge- kutta-fehlberg approximation method to solve the resulting non-linear equation.

Sufficient conditions for oscillation of a certain class of nonlinear third-order differential equations are found. In this paper we considear a nonlinear third-order differential equation of the form y′′′ + q(t)y′ = f(t, y, y′, y′′) (1) where (i) q, q′ ∈ C ( (a,∞) ) for some a with 0 < a < ∞, (ii) f ∈ C ( (a,∞)×R3 ) , t ∈ (a,∞), and y1, y2, y3 ∈ R and f(t, y1, y2, y3)y1 < 0 for all t ∈ (a,∞) a...

ABSTRACT In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems a...

We obtain iso-spectral Euler-Bernoulli beams by using factorization and Lie symmetry techniques. The canonical Euler-Bernoulli beam operator is factorized as the product of a second-order linear differential operator and its adjoint. The factors are then reversed to obtain iso-spectral beams. The factorization is possible provided the coefficients of the factors satisfy a system of non-linear o...