::title::High-Order Local Absorbing Boundary Conditions for Heat Equation in Unbounded Domains
::author::1::Xiaonan Wu
::author::2::Jiwei Zhang
::address::1::Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong, China
::address::2::Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
::email::xwu@hkbu.edu.hk, jwzhang@math.hkbu.edu.hk
::receive::Received 2009-8-19 Accepted 2010-1-20
::online::Available online 2010-9-20
::DOI::10.4208/jcm.1004-m3195
::keywords::Heat equation, High-order method, Absorbing boundary conditions, Parabolic problems in unbounded domains.
::ams::65M06, 65M12, 65M15.
::abstract::
With the development of numerical methods the numerical computations require higher 
and higher accuracy. This paper is devoted to the high-order local absorbing boundary 
conditions (ABCs) for heat equation. We proved that the coupled system yields a stable 
problem between the obtained  high-order local ABCs and the partial differential 
equation in the computational domain. This method has been used widely in wave 
propagation models only recently. We extend the spirit of the methodology to parabolic 
ones, which will become a basis to design the local ABCs for a class of nonlinear PDEs. 
Some numerical tests show that the new treatment is very efficient and tractable.