in recent years, numerous approaches have been applied for finding the solutions of functional equations. one of them is the optimal homotopy asymptotic method. in current paper, this method has been applied for obtaining the approximate solution of fisher equation. the reliability of the method will be shown by solving some examples of various kinds and comparing the obtained outcomes with the ...

The objective of this study is to demonstrate the successful application of an approximate dynamic programming approach in deriving effective operational strategies for the relocation of empty containers in the containerized sea-cargo industry. A dynamic stochastic model for a simple two-ports two-voyages (TPTV) system is proposed first to demonstrate the effectiveness of the approximate optima...

Spherical splines are used to define approximate solutions to strongly elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by using Galerkin method. We prove optimal convergence (in Sobolev norms) of the approximate solution by spherical splines to the exact solution. Our numerical results underlie the theoretical res...

In this paper, the optimal adaptive leader-follower consensus of linear continuous time multi-agent systems is considered. The error dynamics of each player depends on its neighbors’ information. Detailed analysis of online optimal leader-follower consensus under known and unknown dynamics is presented. The introduced reinforcement learning-based algorithms learn online the approximate solution...

In this paper, a new approach for finding an approximate solution for discrete optimal control problems is introduced. In this method the problem is transformed to a continuous optimal control problem whose solution may give rise to a good approximate solution for the original problem. Then, a measure-theoretical approach is applied to solve the new problem. The method is extended to solve time...

Spherical splines are used to define approximate solutions to strongly elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by using Galerkin method. We prove optimal convergence (in Sobolev norms) of the approximate solution by spherical splines to the exact solution. Our numerical results underlie the theoretical res...

In this paper, we used the Optimal Homotopy Asymptotic Method (OHAM) to find the approximate solution of seventh order linear and nonlinear boundary value problems. The approximate solution using OHAM is compared with Variational Iteration Method (VIM) and exact solutions, an excellent agreement has been observed. The approximate solution of the equations is obtained in terms of convergent seri...

Regularized empirical risk minimization problems are fundamental tasks in machine learning and data analysis. Many successful approaches for solving these problems are based on a dual formulation, which often admits more efficient algorithms. Often, though, the primal solution is needed. In the case of regularized empirical risk minimization, there is a convenient formula for reconstructing an ...