Method of Infinite System of Equations for Problems in Unbounded Domains

[摘要] Many problems of mechanics and physics are posed in unbounded(or infinite) domains. For solving these problems one typically limitsthem to bounded domains and find ways to set appropriate conditionson artificial boundaries or use quasi-uniform grid that maps unboundeddomains 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 forsome one-dimensional problems. The problems are reduced to infinitesystem of linear equations. A method for obtaining approximate solution with a given accuracy is proposed. Numerical experiments forseveral examples show the effectiveness of the offered method.

[学科分类] 应用数学