Browsing by Author "Degla, Guy"
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Item Fitted Operator Average Finite Difference Method(Research Gate, 2019-10) Bullo, Tesfaye Aga; File, Gemechis; Degla, GuyIn this paper, we study a fitted operator average finite difference method for solving singularly perturbed parabolic convection-diffusion problems with boundary layer at right side. After discretizing the solution domain uniformly, the differential equation is replaced by average finite difference approximation which gives system of algebraic equation at each time levels. The stability and consistency of the method established very well to guarantee the convergence of the method. Furthermore, some numerical results are given to support our theoretical results and to validate the betterment of using fitted operator methods.Item Optimal Control Governed by Stochastic Elliptic Equations with Regular States(Hikari Ltd, 2019-08-17) Affognon, Steeven Belvinos; Ngare, Philip; Degla, GuyThis study deals with an optimal control problem subject to a stochastic elliptic equation with Dirichlet boundary condition and in which the state process is regular on a stochastic Hilbert space. We prove the existence and uniqueness of the optimal control and provide furthermore necessary and sufficient optimality conditions. The optimal solution is obtained in the case where there is no constraint. Our method is based on variational theory of elliptic boundary problems in Hilbert spaces