This paper deals with the numerical solutions of boundary value problems by patched segmented collocation method. The method examined the numerical solutions of boundary value problems after the whole intervals of consideration have been partitioned into various sub-intervals and the solutions are sought in the various subintervals and then matched together using Chebyshev polynomials as the ba...

In this paper an accurate method to construct the bidiagonal factorization of collocation and Wronskian matrices Jacobi polynomials is obtained used compute with high relative accuracy their eigenvalues, singular values inverses. The particular cases Legendre polynomials, Gegenbauer Chebyshev first second kind rational are considered. Numerical examples included.

ÐHighly-accurate solutions for the lid-driven cavity ̄ow are computed by a Chebyshev collocation method. Accuracy of the solution is achieved by using a substraction method of the leading terms of the asymptotic expansion of the solution of the Navier±Stokes equations in the vicinity of the corners, where the velocity is discontinuous. Critical comparison with former numerical experiments con®r...

In this paper we consider hyperbolic initial value problems subject to periodic boundary conditions with nonsmooth data. We show that if we filter the data and solve the problem by the Galerkin-Collocation method, recently proposed by us, then we can recover pointwise values with spectral accuracy, provided that the actual solution is piecewise smooth. For this we have to perform a local smooth...

We present in this paper several extremely efficient and accurate spectral-Galerkin methods for secondand fourth-order equations in polar and cylindrical geometries. These methods are based on appropriate variational formulations which incorporate naturally the pole condition(s). In particular, the computational complexities of the Chebyshev–Galerkin method in a disk and the Chebyshev–Legendre–...

In this research paper, an improved Chebyshev-Gauss-Lobatto pseudospectral approximation of nonlinear Burger-Huxley and Fitzhugh- Nagumo equations have been presented. The method employs chebyshev Gauss-Labatto points in time and space to obtain spectral accuracy. The mapping has introduced and transformed the initial-boundary value non-homogeneous problem to homogeneous problem. The main probl...