Theoretical Aspects of the Method of Splitting and Artificial Boundary Conditions

The paper is dedicated to the development and analysis of a general methodology for constructing artificial boundary conditions (ABCs ) for numerical solution to differential problems in unbounded domains. Our approach is essentially based on the employment of the techniques of time and dimensional splitting coupled with spline approximations, which unlike all other ABCs-constructing methods allows to obtain exact, local, and geometrically uncritical artificial boundary conditions. The methodology is applied to and studied on the linear advection-diffusion-reaction equation