Method of Infinite System of Equations for Problems in Unbounded Domains

Abstract

Many problems of mechanics and physics are posed in unbounded (or infinite) domains. For solving these problems one typically limits them to bounded domains and find ways to set appropriate conditions on artificial boundaries or use quasi-uniform grid that maps unbounded domains to bounded ones. Differently from the above methods we approach to problems in unbounded domains by infinite system of equations. In this paper we present starting results in this approach for some one-dimensional problems. The problems are reduced to infinite system of linear equations. A method for obtaining approximate solution with a given accuracy is proposed. Numerical experiments for several examples show the effectiveness of the offered method.

A Second Order Finite-Difference Ghost-Point Method for Elasticity Problems on Unbounded Domains with Applications to Volcanology

“…In some cases, the choice of ABCs is not unique [22,44,48] and strongly affects the solutions. A similar approach has been recently adopted in [39]: the problem is transformed into an infinite system of equations and a careful convergence theory suggests where to perform the truncation.…”