First order spectral perturbation theory of square singular matrix polynomials

First order spectral perturbation theory of square singular matrix pencils

Let H(λ) = A0 + λA1 be a square singular matrix pencil, and let λ0 ∈ C be an eventually multiple eigenvalue of H(λ). It is known that arbitrarily small perturbations of H(λ) can move the eigenvalues of H(λ) anywhere in the complex plane, i.e., the eigenvalues are discontinuous functions of the entries of A0 and A1. Therefore, it is not possible to develop an eigenvalue perturbation theory for a...

A spectral method based on Hahn polynomials for solving weakly singular fractional order integro-differential equations

In this paper, we consider the discrete Hahn polynomials and investigate their application for numerical solutions of the fractional order integro-differential equations with weakly singular kernel .This paper presented the operational matrix of the fractional integration of Hahn polynomials for the first time. The main advantage of approximating a continuous function by Hahn polynomials is tha...

Singular perturbation theory

When we apply the steady-state approximation (SSA) in chemical kinetics, we typically argue that some of the intermediates are highly reactive, so that they are removed as fast as they are made. We then set the corresponding rates of change to zero. What we are saying is not that these rates are identically zero, of course, but that they are much smaller than the other rates of reaction. The st...

Geometric Singular Perturbation Theory

Bernoulli matrix approach for matrix differential models of first-order

The current paper contributes a novel framework for solving a class of linear matrix differential equations. To do so, the operational matrix of the derivative based on the shifted Bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. An error estimation of presented method is provided. Numerical experiments are...