In this paper, a spectral collocation approach based on the rational Chebyshev functions for solving the axisymmetric stagnation point flow on an infinite stationary circular cylinder is suggested. The Navier-Stokes equations which govern the flow, are changed to a boundary value problem with a semi-infinite domain and a third-order nonlinear ordinary differential equation by applying proper si...

Collocation has always been an important issue in language research, especially in Chinese language researches. Chinese is an isolated language, which lacks morphological changes.Establishing a relatively complete dictionary of Chinese collocation will be a great contribution to Chinese study and research. Collocation plays a significant supporting role in many fields of NLP, such as informatio...

In this paper, we develop a Jacobi-Gauss-Lobatto collocation method for solving the nonlinear fractional Langevin equation with three-point boundary conditions. The fractional derivative is described in the Caputo sense. The shifted Jacobi-Gauss-Lobatto points are used as collocation nodes. The main characteristic behind the Jacobi-Gauss-Lobatto collocation approach is that it reduces such a pr...

We analyze the convergence behavior of collocation schemes applied to approximate solutions of BVPs in nonlinear index 1 DAEs, which exhibit a critical point at the left boundary. Such a critical point of the DAE causes a singularity in the inherent nonlinear ODE system. In particular, we focus on the case when the inherent ODE system is singular with a singularity of the first kind and apply p...

In this investigation, the Sinc collocation method based on double exponential transformation is developed to solve the Troesche's problem. Properties of this method are utilized to reduce the system of strongly nonlinear two point boundary value problem to same nonlinear algebraic equations. Combining double exponential transformation through Sinc collocation method causes the remarkable resul...

We present a meshfree generalized finite difference method for solving Poisson's equation with diffusion coefficient that contains jump discontinuities up to several orders of magnitude. To discretize the operator, we formulate strong form uses smearing discontinuity; and conservative formulation based on locally computed Voronoi cells. Additionally, propose novel enforcing Neumann boundary con...

A more careful count of the operations involved in solving the linear system associated with collocation of a two-point boundary value problem using rough splines reverses results recently reported by others in this journal. In addition, it is observed that the use of the technique of "condensation of parameters" can decrease the computer storage required. Furthermore, the use of a particular h...

We develop spectral collocation methods for fractional differential equations with variable order with two end-point singularities. Specifically, we derive three-term recurrence relations for both integrals and derivatives of the weighted Jacobi polynomials of the form 1 x μ1 1 Æ x 2P a,b j x a, b, μ1, μ2 Æ1 , which leads to the desired differentiation matrices. We apply the new differentiation...