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...

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.

In this paper we discuss the collocation method for a large class of Fredholm linear integro-differential equations. It will be shown that, when a certain higher order interpolation operation is added to the collocation solution of this equation, the new approximations will, under suitable assumptions, admit a multiterm error expansion in even powers of the step-size h. Based on this expansion,...

We introduce a single patch collocation method in order to compute solutions of initial value problems of partial differential equations whose spatial domains are 3spheres. Besides the main ideas, we discuss issues related to our implementation and analyze numerical test applications. Our main interest lies in cosmological solutions of Einstein’s field equations. Motivated by this, we also elab...

In this paper, we propose a natural collocation method with exact imposition of mixed boundary conditions based on a generalized Gauss-Lobatto-Legendre-Birhoff quadrature rule that builds in the underlying boundary data. We provide a direct construction of the quadrature rule, and show that the collocation method can be implemented as efficiently as the usual collocation scheme for PDEs with Di...

This work presents an initial investigation on how to distinguish collocations from free combinations. The assumption is that , while free combinations can be literally translated, the overall meaning of collocations is different from the sum of the translation of its parts. Based on that, we verify whether a machine translation system can help us perform such distinction. Results show that it ...

A collocation method is presented for numerical solution of a typical integral equation Rh := R D R(x, y)h(y)dy = f(x), x ∈ D of the class R, whose kernels are of positive rational functions of arbitrary selfadjoint elliptic operators defined in the whole space R, and D ⊂ R is a bounded domain. Several numerical examples are given to demonstrate the efficiency and stability of the proposed meth...