a computational method for numerical solution of a nonlinear volterra and fredholm integro-differentialequations of fractional order based on chebyshev cardinal functions is introduced. the chebyshev cardinaloperational matrix of fractional derivative is derived and used to transform the main equation to a system ofalgebraic equations. some examples are included to demonstrate the validity and ...

In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Il...

Newton-Krylov methods, primarily using the Jacobian-Free Newton-Krylov (JFNK) approximation, are examined as an alternative to the traditional power iteration method for the calculation of the fundamental eigenmode in reactor analysis applications based on diffusion theory. One JFNK approach can be considered an acceleration technique for the standard power iteration as it is “wrapped around” t...

A stochastic version of a stationary linear iterative solver may be designed to converge in distribution to a probability distribution with a specified mean μ and covariance matrix A−1. A common example is Gibbs sampling applied to a multivariate Gaussian distribution which is a stochastic version of the Gauss-Seidel linear solver. The iteration operator that acts on the error in mean and covar...

A coupled pair of harmonic equations is solved by the application of Chebyshev acceleration to the Jacobi, Gauss-Seidel, and related iterative methods, where the Jacobi iteration matrix has purely imaginary (or zero) eigenvalues. Comparison is made with a block SOR method used to solve the same problem. Introduction. In [4], we proposed a general block SOR method for solving the biharmonic equa...

We propose a restarted Arnoldi's method with Faber polynomials and discuss its use for computing the rightmost eigenvalues of large non hermitian matrices. We illustrate, with the help of some practical test problems, the beneet obtained from the Faber acceleration by comparing this method with the Chebyshev based acceleration. M ethode d'Arnoldi-Faber pour les probl emes aux valeurs propres no...

The aim of this paper is to use recurrence relations instead of majorizing sequences to establish the semilocal convergence of a continuation method combining Chebyshev method and Convex acceleration of Newton’s method for solving nonlinear equations in Banach spaces under the assumption that the first Fréchet derivative satisfies the Lipschitz continuity condition. An existence-uniqueness theo...

The ranking of genes plays an important role in biomedical research. The GeneRank method of Morrison et al. [11] ranks genes based on the results of microarray experiments combined with gene expression information, for example from gene annotations. The algorithm is a variant of the well known PageRank iteration, and can be formulated as the solution of a large, sparse linear system. Here we sh...

in this paper, an effective direct method to determine the numerical solution of linear and nonlinear fredholm and volterra integral and integro-differential equations is proposed. the method is based on expanding the required approximate solution as the elements of chebyshev cardinal functions. the operational matrices for the integration and product of the chebyshev cardinal functions are des...