In this paper, we develop domain decomposition spectral method for mixed inhomogeneous boundary value problems of high order differential equations defined on unbounded domains. We introduce an orthogonal family of new generalized Laguerre functions, with the weight function x , α being any real number. The corresponding quasiorthogonal approximation and Gauss-Radau type interpolation are inves...

therefore the damping layer has to be large enough to prevent reentrant waves at the physical boundary. Hence In this paper we develop a method for the simulation of wave propagation on artificially bounded domains. The acoustic wave the approach is not only costly in terms of memory requireequation is solved at all points away from the boundaries by a ments but also it is not very flexible. In...

An efficient Spectral Collocation method based on the shifted Legendre polynomials was applied to get solution of heat transfer of a micropolar fluid through a porous medium with radiation. A similarity transformation is applied to convert the governing equations to a system of nonlinear ordinary differential equations. Then, the shifted Legendre polynomials and their operational matrix of deri...

Collocation methods are a well-developed approach for the numerical solution of smooth and weakly singular Volterra integral equations. In this paper, we extend these methods through the use of partitioned quadrature based on the qualocation framework, to allow the efficient numerical solution of linear, scalar Volterra integral equations of the second kind with smooth kernels containing sharp ...