J.L. Morera

A closed-form solution of singular regular higher-order difference initial and boundary value problems

In this paper existence conditions and a closed-form expression for solutions of coupled singular systems of higher-order difference equations are given. The approach avoids the computational drawbacks derived from the standard approach based on the consideration of an equivalent first-order system.

On convergent linear multistep matrix methods

In this paper a sufficient condition in order to a linear multistep matrix method for computing numerically initial value differential matrix problems be convergent is given.

Construction and computation of variable coefficient sylvester differential problems

In this paper, initial value problems for Sylvester differential equations X′(t) = A(t)X(t) + X(t)B(t) + F(t), with analytic matrix coefficients are considered. First, an exact series solution of the problem is obtained. Given a bounded domain Ω and an admissible error ϵ, a finite analytic-numerical series solution is constructed, so that the error with respect to the exact series solution is uniformly upper bounded by ϵ in Ω. An iterative procedure for the construction of the approximate solutions is included.

Numerical multisteps matrix methods for Y ′′ =f t,Y

Abstract In this paper, numerical multistep matrix methods for solving coupled systems of second order differential equations are proposed. These methods permit the simultaneous computation of all the entries of a coupled differential system using algebraic symbolic languages. Error bounds for the discretization error in terms of the data are given. The proposed methods avoid the increase of the computational cost derived from the standard transformation of the differential problem into an extended first order system.

Computable explicit bounds for the discretization error of variable stepsize multistep methods

Abstract This paper deals with the achievement of explicit computable bounds for the global discretization error of variable stepsize multistep methods which are perturbation of strongly stable fixed stepsize methods. The approach is based on the study of the growth of solutions of certain variable coefficient difference equations satisfied by the global discretization error.

The stability of parametricdifference linear systems

Abstract In this paper, the concepts of uniform stability and fixed-station stability of parametricdifference linear systems are introduced in order to guarantee the boundness of solutions for such systems. Spectral sufficient conditions for stability of parametric differential linear systems are given.

Singular perturbations for coupled second order boundary value difference systems

In this paper singular perturbations for coupled second order boundary value difference systems with a small parameter are studied. The asymptotic development of the solution of non-homogeneous boundary value problems related to them and approximations of the exact solution are obtained.

Higher order implicit multistep methods for matrix differential equations

Abstract This paper proposes implicit multistep matrix methods for the numerical solution of stiff initial value matrix problems. The study of matrix difference equations involving the matrix coefficients of the multistep method permits one to obtain convergence results, as well as bounds for the global discretization error in terms of the data. An illustrative example is included.

Singular perturbations for systems of second order difference equations

Abstract This paper studies the asymptotic behavior of singular perturbations for systems of second order linear difference equations with a small parameter.