In this paper, a well-conditioned collocation method is constructed for solving general p th
order linear differential equations with various types of boundary conditions. Based on a …

In this paper we describe a generic spectral Petrov–Galerkin method that is sparse and
strictly banded for any linear ordinary differential equation with polynomial coefficients. The …

In this paper, the recursive approach of the Tau method is developed for numerical solution
of Abel–Volterra type integral equations. Due to the singular behavior of solutions of these …

In this paper, we construct a set of non-polynomial basis functions from a generalised
Birkhoff interpolation problem involving the operator: L _ λ= d^ 2/dx^ 2-λ^ 2 L λ= d 2/dx 2-λ 2 …

A new efficient Chebyshev–Petrov–Galerkin (CPG) direct solver is presented for the second
order elliptic problems in square domain where the Dirichlet and Neumann boundary …

As the Tau method, like many other numerical methods, has the limitation of using a fixed
step size with some high degree (order) of approximation for solving initial value problems …

In 1958 the first US satellite, Explorer 1, reported unexpectedly low cosmic ray counts
around the Earth. The data was examined by a research team led by space physicist James …

A matrix representation of integration for arbitrary grids is introduced. Suitable results are
then obtained to be used along with differentiation matrix preconditioner to implement …

In this work, we investigate the new preconditioner of the Tau method, introduced by
Ghoreishi and Mohammad Hosseini [13], on systems of ODEs. With a different and relatively …

In the first portion of this thesis, a new well-conditioned collocation method for solving
differential equations based on Birkhoff interpolation is presented. The collocation schemes …