Inthispaper,wesolveHamilton-Jocobi-Bellman(HJB)equationsarisinginoptimalcontrolproblems usingHomotopyPerturbationTransformMethod(HPTM).Theproposedmethodisacombinedform oftheLaplaceTransformationMethodwiththeHomotopyPerturbationMethodtoproduceahighly effectivemethodtohandlemanyproblems. ApplyingtheHPTM,solutionprocedurebecomeseasier, simplerandmorestraightforward. Someillustrativeexamplesaregive...

The classical Coulomb potential and force can be calculated efficiently using fast multi-pole methods. Effective quantum potentials, however, describe the physics of electron transport in semiconductors more precisely. Such an effective quantum potential was derived previously for the interaction of an electron with a barrier for use in particle-based Monte Carlo semiconductor device simulators...

We study a 2-and a 4-dimensional nearly integrable symplectic maps using a singular perturbation method. Resonance island structures in the 2-and 4-dimensional maps are successfully obtained. Those perturbative results are numerically confirmed. Chaotic Hamiltonian systems with many degrees of freedom are not only of interest in view of the foundation of dynamical system, but also have a lot of...

I discuss the possibility of using classical field theory to approximate hot, realtime quantum field theory. I calculate, in a scalar theory, the classical two point and four point function in perturbation theory. The counterterms needed to make the classical correlation functions finite are dictated by the superrenormalizability of the static theory. The classical expressions approximate the q...

In this dissertation, we discuss two methods developed during my PhD study to simulate electron transfer systems. The first method, the semi-classical approximation, is derived from the stationary phase approximation to the path integral in the spin-coherent representation. The resulting equation of motion is a classical-like ordinary differential equation subject to a two-ended boundary condit...

In this work, the newly developed optimal perturbation iteration technique with Laplace transform is applied to generalized regularized long wave equations a new fractional operator obtain approximate solutions. We classical differential form by using Atangana-Baleanu derivative which defined Mittag-Leffler function. To show efficiency of proposed method, numerical example given for different v...

The steady motion of a symmetric, finite core size, counterrotating vortex pair is characterized by circulation r, a velocity V, and a spacing 2xooo In the classical limit of a point vortex, the normalized velocity, vx~/r, is 1/(41T). The effect of finite core size is to reduce the normalized velocity below the value for a point vortex. The flow is governed by a single geometrical parameter R/x...

The exact eigenvalues of the infinite set of conserved charges on the multiparticle states in affine Toda theories are determined. This is done by constructing a free field realization of the Zamolodchikov-Faddeev algebra in which the conserved charges are realized as derivative operators. The resulting eigenvalues are renormalization group (RG) invariant, have the correct classical limit and p...

In this paper, the solution of the evolutionaryfourth-order in space, Sivashinsky equation is obtained by meansof homotopy perturbation method (textbf{HPM}). The results revealthat the method is very effective, convenient  and quite accurateto systems of nonlinear partial differential equations.

In this paper, we study semi-analytical methods entitled Homotopy pertourbation method (HPM) to solve fuzzy impulsive fractional differential equations based on the concept of generalized Hukuhara differentiability. At the end first of Homotopy pertourbation method is defined and its properties are considered completely. Then econvergence theorem for the solution are proved and we will show tha...