in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

Abstract. We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Po...

in this paper, we introduce the new class of implicit l-stable generalized hybrid methods forthe numerical solution of first order initial value problems. we generalize the hybrid methodswith utilize ynv directly in the right hand side of classical hybrid methods. the numericalexperimentation showed that our method is considerably more efficient compared to wellknown methods used for the numer...