In this paper a version of the optimal homotopy asymptotic method (OHAM) has been proposed and applied to nonlinear oscillators with discontinuities. The main objective was to obtain highly accurate analytical solutions for a particular antisymmetric constant force oscillator using this new procedure. The proposed procedure proved to be very effective and accurate and did not require linearizat...

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

In this paper, the optimal homotopy analysis method is applied to find the solitary wave solutions of the Kuramoto-Sivashinsky equation. With three auxiliary convergence-control parameters, whose possible optimal values can be obtained by minimizing the averaged residual error, the method used here provides us with a simple way to adjust and control the convergence region of the solution. Compa...

The multi-homogenous homotopy continuation method is one of the most efficient approaches in finding all isolated solutions of polynomial systems. A different partition of variables leads to a different homotopy system. The homotopy using the optimal partition of variables reduces the computational cost in curve following to the minimum. However, finding the optimal variable partition is likely...

in this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. the homotopy analysis method (ham) is used for solving this equation. several examples are given to reconfirm the efficiency of these algorithms. the results of applying this procedure...