TY - JOUR
T1 - Convergence of difference scheme for heat equation in unbounded domains using artificial boundary conditions
AU - Wu, Xiaonan
AU - Sun, Zhi-Zhong
N1 - Funding Information:
* Corresponding author. E-mail addresses: [email protected] (X. Wu), [email protected] (Z.-Z. Sun). 1 Research is supported in part by RGC of Hong Kong and FRG of Hong Kong Baptist University. 2 Research is supported in part by RGC of Hong Kong and FST of Southeast University.
PY - 2004/8
Y1 - 2004/8
N2 - The finite difference solution of one-dimensional heat conduction equation in unbounded domains is considered. An artificial boundary is introduced to make the computational domain finite. On the artificial boundary an exact boundary condition is applied to reduce the original problem to an initial-boundary value problem. A finite difference scheme is constructed by the method of reduction of order. It is proved that the finite difference scheme is uniquely solvable, unconditionally stable and convergent with the order 2 in space and the order 3/2 in time under an energy norm. A numerical example demonstrates the theoretical results.
AB - The finite difference solution of one-dimensional heat conduction equation in unbounded domains is considered. An artificial boundary is introduced to make the computational domain finite. On the artificial boundary an exact boundary condition is applied to reduce the original problem to an initial-boundary value problem. A finite difference scheme is constructed by the method of reduction of order. It is proved that the finite difference scheme is uniquely solvable, unconditionally stable and convergent with the order 2 in space and the order 3/2 in time under an energy norm. A numerical example demonstrates the theoretical results.
KW - Artificial boundary condition
KW - Finite difference
KW - Heat equation
KW - Unbounded domain
UR - http://www.scopus.com/inward/record.url?scp=2442665695&partnerID=8YFLogxK
U2 - 10.1016/j.apnum.2004.01.001
DO - 10.1016/j.apnum.2004.01.001
M3 - Journal article
AN - SCOPUS:2442665695
SN - 0168-9274
VL - 50
SP - 261
EP - 277
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
IS - 2
ER -