Diffusion-type problems in (nearly) unbounded domains play important roles in various
fields of fluid dynamics, biology, and materials science. The aim of this paper is to construct …

We are concerned with the numerical solution of a nonlocal wave equation in an infinite two-
dimensional space. The contribution of this paper is the derivation of an absorbing boundary …

Construction of absorbing boundary conditions (ABCs) for nonlocal models is generally
challenging, primarily due to the fact that nonlocal operators are commonly associated with …

This paper is concerned with numerical approximations of a nonlocal heat equation define
on an infinite domain. Two classes of artificial boundary conditions (ABCs) are designed …

The stability and error analysis of a second-order fast approximation are considered for the
one-dimensional local and nonlocal diffusion equations in the unbounded spatial domain …

The aim of this paper is to design some accurate artificial boundary conditions for the semi-
discretized linear Schrödinger and heat equations in rectangular domains. The Laplace …

In this paper, we derive the exact artificial boundary conditions for one-dimensional reaction-
diffusion-advection equation on an unbounded domain. By employing the Laplace …

An artificial boundary method is developed for solving the one-dimensional advection
diffusion equation in the real line. In order to construct a fully discrete fast numerical …

Abstract In the Enhanced Geothermal System (EGS), the flow state of the fracture of the
thermal reservoir (granite) is important for heat transfer. In this paper, the effects of reservoir …

The artificial boundary method is applied to numerically solve the nonlinear Schrödinger
equation with damping term on unbounded domain. A novel transformation is developed to …