We present optimal error estimates for spectral Petrov–Galerkin methods and spectral collocation methods for linear fractional ordinary differential equations with initial value on a finite interval. We also develop Laguerre spectral Petrov–Galerkin methods and collocation methods for fractional equations on the half line. Numerical results confirm the error estimates.

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...

A spectral relaxation method used with bivariate Lagrange interpolation is used to find numerical solutions for the unsteady three-dimensional flow problem of an Oldroyd-B fluid with variable thermal conductivity and heat generation. The problem is governed by a set of three highly coupled nonlinear partial differential equations. The method, originally used for solutions of systems of ordinary...

We consider hyperbolic systems of conservation laws which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level we introduce a domain decomposition method based on an iteration-by-subdomain procedure yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The m...

Numerical and analytical solutions of Stokes theory couple stress fluid under the effects constant, space, variable viscosity in inclined channel are discussed here. The considered is described mathematically with definition tensor. dimensional form boundary value problem transformed into dimensionless by defining quantities then solved help perturbation technique. expressions velocity temperat...

This paper focuses on the task of collocation polarity disambiguation. The collocation refers to a binary tuple of a polarity word and a target (such as ⟨long, battery life⟩ or ⟨long, startup⟩), in which the sentiment orientation of the polarity word (“long”) changes along with different targets (“battery life” or “startup”). To disambiguate a collocation’s polarity, previous work always turned...

A spectral vanishing viscosity technique (SVV) is presented for the simulation of 3D turbulent incompressible flows within a rotor–stator cavity. One characteristic of this technique is that the SVV is active only for the short length scales, a feature which is reminiscent of Large Eddy Simulation models. The Spectral Vanishing Viscosity, first introduced by E. Tadmor for the inviscid Burgers e...