In this paper, we propose mixed generalized Hermite-Legendre spectral method for partial differential equation set in an infinite strip. We investigate mixed generalized Hermite-Legendre approximation. We propose the new algorithm for various boundary condition problems with variable coefficient. The global convergence of proposed algorithms is proved. Numerical results demonstrate the spectral...

Abstract We discuss the problem of unique determination finite free discrete Schrödinger operator from its spectrum, also known as Ambarzumian problem, with various boundary conditions, namely any real constant condition at zero and Floquet conditions angle. Then we prove following Ambarzumian-type mixed inverse spectral problem: diagonal entries except first second ones a set two consecutive e...

We consider the numerical solution of elliptic boundary value problems by mixed nite element discretizations on simplicial triangulations. Emphasis is on the eecient iterative solution of the discretized problems by multilevel techniques and on adaptive grid reenement. The iterative process relies on a preconditioned conjugate gradient iteration in a suitably chosen subspace with a multilevel p...

The aim of this paper is solving nonlinear Volterra-Fredholm fractional integro-differential equations with mixed boundary conditions‎. ‎The basic idea is to convert fractional integro-differential equation to a type of second kind Fredholm integral equation‎. ‎Then the obtained Fredholm integral equation will be solved with Nystr"{o}m and Newton-Kantorovitch method‎.  ‎Numerical tests for demo...

We consider the homogenization of the Navier-Stokes equation, set in a channel with a rough boundary, of small amplitude and wavelength ǫ. It was shown recently that, for any non-degenerate roughness pattern, and for any reasonable condition imposed at the rough boundary, the homogenized boundary condition in the limit ε = 0 is always no-slip. We give in this paper error estimates for this homo...