This paper is concerned with the design of artificial boundary conditions (ABCs) for nonlinear time fractional Burgers’ equation on unbounded domains, that describes the propagation of many kinds of waves in physics. It is a major challenge to design appropriate ABCs to obtain the numerical solution and simulate the real physical phenomena, owing to the unboundedness of the physical domain, nonlocality and nonlinearity. The ABCs on the introduced artificial boundaries are constructed by applying the ideas of operator splitting approach and artificial boundary method to obtain a reduced initial boundary value problem on the truncated computational domain, which can be solved by the finite difference method efficiently. The boundedness and convergence are rigorously analyzed. Numerical simulations are presented to validate accuracy and feasibility of our proposed method.

本文涉及无界域上非线性时间分数Burgers方程的人工边界条件（ABC）的设计，该方程描述了物理学中多种波的传播。由于物理域的无限性，非局部性和非线性，设计适当的ABC来获得数值解并模拟真实的物理现象是一个重大挑战。通过引入算子分解法和人工边界方法的思想，构造了引入的人工边界上的ABC，从而在截断的计算域上获得了减小的初始边界值问题，可以通过有限差分法有效地解决该问题。严格分析了有界性和收敛性。