A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic fields. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary...

In this paper we explain on various examples the “phantom tracking” method, a method which can be used to stabilize nonlinear control systems modeled by ordinary differential equations or partial differential equations. We show how it can handle global controllability, homogeneity issues or fast stabilization.

In this paper we propose a class of second derivative multistep methods for solving some well-known classes of LaneEmden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-...

We consider the Cauchy problem on the positive half-line for the differential-delay equation ü(t) + 2c0(t)u̇(t) + c1(t)u̇(t − h) + d0(t)u(t) + d1(t)u(t − h) + d2(t)u(t − 2h) = 0 where ck(t), dj(t) (t ≥ 0; k = 0, 1; j = 0, 1, 2) are continuous functions. Conditions providing the positivity of the Green function and a lower bound for that function are derived. Our results are new even in the case o...

In this article we review the Adomian decomposition method (ADM) and its modifications including different modified and parametrized recursion schemes, the multistage ADM for initial value problems as well as the multistage ADM for boundary value problems, new developments of the method and its applications to linear or nonlinear and ordinary or partial differential equations, including fractio...

The unsteady stagnation point flow and heat transfer with prescribed flux towards a stretching and shrinking sheet with viscous dissipation is studied. Similarity transformation is adopted to initially convert the governing differential equations into nonlinear ordinary differential equations. The two-point boundary value ordinary differential equations (ODE) are subsequently converted into par...