Reinforcement Problems for Elliptic Equations

Analytic solutions for the Stephen's inverse problem with local boundary conditions including Elliptic and hyperbolic equations

In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. For the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

A numerical method for solving nonlinear partial differential equations based on Sinc-Galerkin method

In this paper, we consider two dimensional nonlinear elliptic equations of the form $ -{rm div}(a(u,nabla u)) = f $. Then, in order to solve these equations on rectangular domains, we propose a numerical method based on Sinc-Galerkin method. Finally, the presented method is tested on some examples. Numerical results show the accuracy and reliability of the proposed method.

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Multi-Grid Methods for Reinforcement Learning in Controlled Diffusion Processes

Reinforcement learning methods for discrete and semi-Markov decision problems such as Real-Time Dynamic Programming can be generalized for Controlled Diffusion Processes. The optimal control problem reduces to a boundary value problem for a fully nonlinear second-order elliptic differential equation of HamiltonJacobi-Bellman (HJB-) type. Numerical analysis provides multigrid methods for this ki...

Existence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight

‎This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight‎. ‎We apply the variational methods to prove the existence of ground state solution‎.