This article proposes a fast and accurate expansion-iterative method for solving second kind linear Volterra integral equations. The method is based on a special representation of vector forms of triangular functions (TFs) and their operational matrix of integration. By using this approach, solving the integral equation reduces to solve a recurrence relation. The approximate solution of integra...

In this work we provide low rank estimations for coordinate sequences of linear recurrent sequences (LRS) of maximal period (MP) over Galois ring R = GR(pn, r), p ≥ 5, r ≥ 2, with numbers s such that s = kr + 2, k ∈ N0.

Analysis of algorithms occasionally requires solving of rst-order two-dimensional linear homogeneous partial di erence equations. We survey solutions to special cases of the linear recurrence equation (am + bn + c)Fm;n = (dm + en + f)Fm 1;n + (gm + hn + i)Fm 1;n 1 in terms of known functions and establish equivalences between unsolved cases. The article also reviews solution techniques used to ...

Serre’s reduction aims at reducing the number of unknowns and equations of a linear functional system (e.g., system of ordinary or partial differential equations, system of differential time-delay equations, system of difference equations). Finding an equivalent representation of a linear functional system containing fewer equations and fewer unknowns generally simplifies the study of its struc...

We derive recurrence relations between phase space expressions in different dimensions by confining some of the coordinates to tori or spheres of radius R and taking the limit as R → ∞. These relations take the form of mass integrals, associated with extraneous momenta (relative to the lower dimension), and produce the result in the higher dimension.

Let q be a prime power and Fq be the finite field with q elements. A q-ary m-sequence is a linear recurrence sequence of elements from Fq with the maximum possible period. A covering array CA(N ; t, k, v) of strength t is a N ×k array with entries from an alphabet of size v, with the property that any N×m subarray has at least one row equal to every possible m-tuple of the alphabet. The coverin...

In this paper, two second order half-linear difference equations are considered. By establishing their connections with a standard half-linear difference equation, we are able to obtain sufficient conditions for existence and nonexistence of eventually positive solutions.

The critical delays of a delay-differential equation can be computed by solving a nonlinear two-parameter eigenvalue problem. The solution of this two-parameter problem can be translated to solving a quadratic eigenvalue problem of squared dimension. We present a structure preserving QR-type method for solving such quadratic eigenvalue problem that only computes real valued critical delays, i.e...

We analyze the Chebyshev iteration in which the linear system involving the splitting matrix is solved inexactly by an inner iteration. We assume that the tolerance for the inner iteration may change from one outer iteration to the other. When the tolerance converges to zero, the asymptotic convergence rate is unaaected. Motivated by this result, we seek the sequence of tolerance values that yi...

This article analyses the asymptotic behaviour of solutions of linear Volterra difference equations. Some sufficient conditions are presented under which the solutions to a general linear equation converge to limits, which are given by a limit formula. This result is then used to obtain the exact asymptotic representation of the solutions of a class of convolution scalar difference equations, w...