Perturbed nonlocal fourth order equations of Kirchhoff type with Navier boundary conditions

Multiplicity Results for Perturbed Fourth-order Kirchhoff-type Problems

Numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type

In this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

Nonlocal Boundary Conditions for the Navier – Stokes Equations

In this paper nonlocal boundary conditions for the Navier–Stokes equations are derived, starting from the Boltzmann equation in the hydrodynamic limit. Basing on phenomenological arguments, two scattering kernels which model non–local interactions between the gas molecules and the wall boundary are proposed. They satisfy the global mass conservation and a generalized reciprocity relation. The a...

Analysis of Fourth-order Accurate Symmetry-preserving Boundary Conditions for the Incompressible Navier-stokes Equations

Abstract. In this paper we investigate symmetry-preserving boundary conditions for a fourth-order symmetry-preserving finite volume method, to able to do accurate turbulence simulations for wind-turbine wake applications. It is found that the use of Dirichlet conditions limits the fourth-order method to (at most) second order. However, on properly chosen non-uniform grids, fourth-order behavior...

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...