Article history: Received 10 March 2014 Received in revised form 12 November 2014 Accepted 1 December 2014 Available online 9 December 2014

The problem of the boundary layer flow of an incompressible viscous fluid over a non-linear stretching sheet is considered. A spectral collocation method is performed in order to find an analytical solution of the governing nonlinear differential equations. The obtained results are finally compared through the illustrative graphs and tables with the exact solution and some well-known results ob...

The numerical solution of boundary value problems for ordinary differential equations on infinite intervals is considered. The infinite interval is cut at a finite, large enough point and additional boundary conditions are posed there. For the solution of the resulting problem, /(-stable symmetric collocation methods are employed. Using the behavior of the solution of the "infinite" problem, me...

In this paper we present the convergence analysis of iterative schemes for solving linear systems resulting from diacretizing multidimensional linear second order elliptic partial differential equations (PDEs) defined in a hyper-parallelepiped n and subject to Dirichlet boundary conditions on some faces of n and Neumann on the others, using a new class of line cubic spline collocation (LeSC) me...

The harmonic Lanczos bidiagonalization method can be used to compute the smallest singular triplets of a large matrix A. We prove that for good enough projection subspaces harmonic Ritz values converge if the columns of A are strongly linearly independent. On the other hand, harmonic Ritz values may miss some desired singular values when the columns of A are almost linearly dependent. Furthermo...

We describe the development of a method for the efficient computation of the smallest singular values and corresponding vectors for large sparse matrices [4]. The method combines state-of-the-art techniques that make it a useful computational tool appropriate for large scale computations. The method relies upon Lanczos bidiagonalization (LBD) with partial reorthogonalization [6], enhanced with ...

This paper concerns a harmonic projection method for computing an approximation to an eigenpair (λ, x) of a large matrix A. Given a target point τ and a subspace W that contains an approximation to x, the harmonic projection method returns an approximation (μ + τ, x̃) to (λ, x). Three convergence results are established as the deviation of x from W approaches zero. First, the harmonic Ritz value...

Lane-Emden differential equations of order fractional has been studied. Numerical solution of this type is considered by collocation method. Some of examples are illustrated. The comparison between numerical and analytic methods has been introduced.

We propose a new method to deal with the essential boundary conditions encountered in deep learning-based numerical solvers for partial differential equations. The trial functions representing by neural networks are non-interpolatory, which makes enforcement of nontrivial matter. Our resorts Nitsche's variational formulation this difficulty, is consistent, and does not require significant extra...