A Chebyshev or Fourier series may be evaluated on the standard collocation grid by the Fast Fourier Transform (FFT). Unfortunately, the FFT does not apply when one needs to sum a spectral series at N points which are spaced irregularly. The cost becomes O(N2) operations instead of the FFT's O(N log N). This sort of "off-grid" interpolation is needed by codes which dynamically readjust the grid ...

A generalized Chebyshev wavelet operational matrix (CWOM) is presented for the solution of nonlinear Riccati differential equations. The operational matrix together with suitable collocation points converts the fractional order Riccati differential equations into a system of algebraic equations. Accuracy and efficiency of the proposed method is verified through numerical examples and comparison...

In this article we study the implementation of the Nonlinear Galerkin method as a multiresolution method when a two-level Chebyshev-collocation discretization is used. A fine grid containing an even number of Gauss-Lobatto points is considered. The grid is decomposed into two coarse grids based on half as many Gauss-Radau points. This splitting suggests a decomposition of the unknowns in low mo...

Stable and accurate surface-wave calculations present a long-standing numerical and analytical challenge to seismologists. In a layered medium, we can describe the surface-wave behavior with harmonic time dependence in terms of an eigenproblem where the eigenvalues and eigenfunctions define the surface-wave modes. Numerous studies have explored diverse numerical approaches to solve this eigenpr...

We propose and analyze the spectral collocation approximation for the partial integrodifferential equations with a weakly singular kernel. The space discretization is based on the pseudo-spectral method, which is a collocation method at the Gauss-Lobatto quadrature points. We prove unconditional stability and obtain the optimal error bounds which depend on the time step, the degree of polynomia...

The von-K arm an nonlinear, dynamic, partial differential system over rectangular domains is considered, and numerically solved using both the Chebyshev-collocation and Legendre-collocation methods for the spatial discretization and the implicit Newmark-b scheme combined with a non-linear fixed point algorithm for the temporal discretization. As the system is non-linear, involving operators of ...

In this paper, we apply the Legendre spectral-collocation method to obtain approximate solutions of nonlinear multiorder fractional differential equations (M-FDEs). The fractional derivative is described in the Caputo sense. The study is conducted through illustrative example to demonstrate the validity and applicability of the presented method. The results reveal that the proposed method is ve...

Article history: Received 10 December 2012 Received in revised form 26 July 2013 Accepted 30 July 2013 Available online 17 August 2013

This article introduces a new method for discretizing and solving integral equation formulations of Maxwell's equations, which achieves spectral accuracy smooth surfaces. The approach is based on hybrid Nyström-collocation using Chebyshev polynomials to expand the unknown current densities over curvilinear quadrilateral surface patches. As an example, proposed strategy applied magnetic field (M...

presents a modiied Chebyshev pseudospec-tral method, involving mapping of the Chebyshev points, for solving rst-order hyperbolic initial boundary value problems. It is conjectured that the time step restriction for the modiied method is O(N ?1) compared to O(N ?2) for the standard Chebyshev pseudospectral method, where N is the number of discretization points in space. In the present paper we s...