1,721,033 research outputs found
On an unusual application of ODEs to solve linear systems
No full textHere we present an unusual iterative method to solve a given (possibly ill-conditioned) linear system, which exploits the solution of an associated vectorial differential equation. The aim of this work is to provide insight into an unusual way of building an iterative method, which does not want to compete with already well established iterative methods, but just introduces a different point of view. The presented method is compared with other well known iterative methods and reported numerical results confirm the effectiveness of this approach
On the representation of close-to-equilibrium solutions of n-dimensional conservative oscillators
No full textWe propose an analytical representation of close-to-equilibrium solutions of nonlinear conservative oscillators with n-degrees
of freedom (n > 2) using semitrigonometric polynomials, given in closed form. A convergence theorem is proved. Moreover we
present an iterative method which implements the proposed representation. Some significant examples are given
About the numerical conservation of first integral by a a class of symmetric methods
No full textWe pesent a class of symmetric methods which are particularly suitable for general conserving systems. Numerical evidence for numerical conservation of first integral within a requested accuracy is provided
About characterization of D-stability by a computer algebra approach
No full textThe concept of D-stability is significant for matrices of any order, especially when they appear in ordinary differential systems modelling physical problems. The problem of characterization of a D-stable matrix was solved for low order matrices only, because of computational complexity required to check conditions assuring D-stability. Here we present an approach based on numerical linear algebra theorems, which provide conditions easily checked by computer algebra
A new efficient approach to the characterization of D-stable matrices
No full textThe concept of D-stability is relevant for stable square matrices of any order, especially when they appear in ordinary differential systems modeling physical problems. Indeed, D-stability was treated from different points of view in the last 50 years, but the problem of characterization of a general D-stable matrix was solved for low-order matrices only (ie, up to order 4). Here, a new approach is proposed within the context of numerical linear algebra. Starting from a known necessary and sufficient condition, other simpler equivalent necessary and sufficient conditions for D-stability are proved. Such conditions turn out to be computationally more appealing for symbolic software, as discussed in the reported examples. Therefore, a new symbolic method is proposed to characterize matrices of order greater than 4, and then it is used in some numerical examples, given in details
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