The Optimal Variational Method (OVM) is introduced and applied for calculating approximate periodic solutions of “truly nonlinear oscillators”.Themain advantage of this procedure consists in that it provides a convenient way to control the convergence of approximate solutions in a very rigorous way and allows adjustment of convergence regions where necessary.This approach does not depend upon a...

We investigate the hard nonresonant excitation of the forced Duffing equation with a positive damping parameter E. Using the symbolic manipulation system MACSYMA, a computer algebra system. we derive the two term perturbation expansion by the method of multiple time scales. The resulting approximate solution is valid for small values of the coefficient e As the damping parameter e increases, th...

There are several reinforcement learning algorithms that yield approximate solutions for the problem of policy evaluation when the value function is represented with a linear function approximator. In this paper we show that each of the solutions is optimal with respect to a specific objective function. Moreover, we characterise the different solutions as images of the optimal exact value funct...

The aim of this paper is by using the fractional complex transform and the optimal homotopy analysis by method (OHAM) to find the analytical approximate solutions for nonlinear partial fractional differential Zakharov-Kuznetsov equation. Fractional complex transformation is proposed to convert nonlinear partial fractional differential Zakharov-Kuznetsov equation to nonlinear partial differentia...

In this paper a numerical method for solving second order fuzzy differential equations under generalized differentiability is proposed. This method is based on the interpolating a solution by piecewise polynomial of degree 4 in the range of solution. Moreover we investigate the existence, uniqueness and convergence of approximate solutions. Finally the accuracy of piecewise approximate method b...

TIle multiple-choice continuous knapsack problem is dermed as follows: maximize z = ~n ~~i CjJ'XiJ' 1=1 J= 1 subject to (1) ~n ~mi aijXij .;;; b, (2) 0 .;;; Xij .;;; I, i = 1,2, ... , n,j = 1. 2, ... , mi, (3) at most one of Xij G = 1,2, ... , mi) 1=1 J=1 is positive for each i = I, 2, ... , n, where n, mi are positive integers and aij are nonnegative integers. In this paper, it is proved that ...

Recently, a couple of approaches have been developed that combine multiobjective optimization with direct discretization methods to approximate trajectories of optimal control problems, resulting in restricted optimization problems of high dimension. The solution set of a multiobjective optimization problem is called the Pareto set which consists of optimal compromise solutions. A common way to...

In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the produ...

In this paper, we consider variational iteration method (VIM) to obtain exact solution to the Fisher’s equation. The variational iteration method is based on Lagrange multipliers for identification of optimal value of parameters in a functional. Using this method, it is possible to find the exact solution or an approximate solution of the problem.

Differential (Ore) type polynomials with “approximate” polynomial coefficients are introduced. These provide an effective notion of approximate differential operators, with a strong algebraic structure. We introduce the approximate Greatest Common Right Divisor Problem (GCRD) of differential polynomials, as a non-commutative generalization of the well-studied approximate GCD problem. Given two ...