Krylov subspace methods for approximating the action of matrix exponentials are analyzed
in this paper. We derive error bounds via a functional calculus of Arnoldi and Lanczos …

This paper reviews various aspects of stiffness in the numerical solution of initial-value
problems for systems of ordinary differential equations. In the literature on numerical …

Restricted Denominator (RD) rational approximations to the matrix exponential operator are
constructed by interpolation in points related to Krylov subspaces associated to a rational …

The integration of semidiscrete approximations for time-dependent problems is encountered
in a variety of applications. The Runge--Kutta (RK) methods are widely used to integrate the …

The numerical contour integral method with hyperbolic contour is exploited to solve space-
fractional diffusion equations. By making use of the Toeplitz-like structure of spatial …

An interpolatory approximation of the matrix exponential based on Faber polynomials -
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In this paper we consider a method based on Faber polynomials for the approximation of
functions of real nonsymmetric matrices. Particular attention is devoted to some functions …

Abstract We prove that Runge–Kutta (RK) methods for numerical integration of arbitrarily
large systems of Ordinary Differential Equations are linearly stable. Standard stability …

In this paper we investigate some practical aspects concerning the use of the restricted-
denominator rational Arnoldi method for the computation of the core functions of exponential …

We consider a Krylov subspace approximation method for the symmetric differential Riccati
equation $\dot {X}= AX+ XA^ T+ Q-XSX $, $ X (0)= X_0 $. The method we consider is based …