无界区域上分数阶 Klein-Gordon 方程的近似人工边界条件-《集美大学学报（自然科学版）》

文章信息/Info

Title:: The Approximate Artificial Boundary Condition for the Fractional Klein-Gordon Equations in Unbounded Domains

Author(s):: ZHU Rongkun; LIANG Zongqi; (School of Science,Jimei University,Xiamen 361021,China)

Keywords:: unbounded domain; time fractional Klein-Gordon equation; artificial boundary conditions; Laplace transform

摘要:: 为了研究无界区域上时间分数阶 Klein-Gordon方程，利用Laplace变换和Lagrange插值，将无界区域上时间分数阶Klein-Gordon方程近似转化为无界区域上整数阶偏微分方程。在此基础上，利用人工边界方法得到3种不同情形下无界区域上整数阶偏微分方程的人工边界条件，从而将无界区域上时间分数阶 Klein-Gordon方程近似转化成有界区域上人工边界条件下整数阶偏微分方程的初边值问题，并证明了人工边界条件下整数阶偏微分方程的稳定性。最后，构造了人工边界条件下整数阶偏微分方程的有限差分格式，并通过数值例子验证该格式的有效性。

Abstract:: In order to study time-fractional Klein-Gordon equation on an unbounded domain,the Laplace transformation and the Lagrange interpolation were used to approximately transform the time-fractional Klein-Gordon equation on the unbounded domain into an integer order partial differential equation on the unbounded domain. On the basis，the artificial boundary method was used to obtain artificial boundary conditions of integer order partial differential equation in three different situations，thereby transforming the approximation problem on the unbounded domain into the initial-boundary value problem with artificial boundary condition on the bounded domain，and prove the stability of the initial-boundary value problem on the bounded domain. Finally，finite difference scheme for the reduced problem in bounded domain was constructed and numerical example showed that artificial boundary method was efficient to solve time-fractional Klein-Gordon equation.