In this paper, a numerical method is proposed to solve FredholmVolterra fractional integro-differential equation with nonlocal boundary conditions. For this purpose, the Chebyshev wavelets of second kind are used in collocation method. It reduces the given fractional integro-differential equation (FIDE) with nonlocal boundary conditions in a linear system of equations which one can solve easily...

We study the linearized stability of shear flow satisfying Navier slip boundary conditions. The Orr-Sommerfeld equation for the plane Poiseuille flow with Navier slip boundary conditions is solved numerically by the Chebyshev collocation method. Our numerical results show that slip at the boundary increases the critical Reynolds number Rc for instability. The dependence of the this critical Rey...

A spectral solution of the RLW equation based on collocation method using Chebyshev polynomials as a basis for the approximate solution is proposed. Test problems, including the motion of a single solitary wave with different amplitudes are used to validate this algorithm which is found to be more accurate than previous ones. The interaction of solitary waves is used to discuss the effect of th...

We present a Python module named PyCheb, to solve the ordinary differential equations by using spectral collocation method. PyCheb incorporates discretization using Chebyshev points, barycentric interpolation and iterate methods. With this Python module, users can initialize the ODEsolver class by passing attributes, including the both sides of a given differential equation, boundary conditions...

The accurate calculation of the sound field is one most concerning issues in hydroacoustics. one-dimensional spectral method has been used to correctly solve simplified underwater acoustic propagation models, but it difficult actual ocean fields using this model due its application conditions and approximation error. Therefore, necessary develop a direct solution for two-dimensional Helmholtz e...

A novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh transform, the original Chebyshev points are mapped into the transformed ones clustered near the singular points of the solution. The results from asymptotic analysis about the singula...

This paper reports a new spectral collocation algorithm for solving time-space fractional partial differential equations with subdiffusion and superdiffusion. In this scheme we employ the shifted Legendre Gauss-Lobatto collocation scheme and the shifted Chebyshev Gauss-Radau collocation approximations for spatial and temporal discretizations, respectively. We focus on implementing the new algor...