A finite difference method for heat equation in the unbounded domain

DOI

10.2991/aest-16.2016.51How to use a DOI?

Keywords

non-homogeneous heat equation; unbounded domain; artificial boundary condition; finite difference method; error estimate.

Abstract

The numerical method of the one-dimensional non-homogeneous heat equation on an unbounded domain is considered. Two exact artificial boundary conditions are applied on two artificial boundaries to limit the original problem onto a bounded computational domain. Then the finite difference method is developed by using the method of the reduction of order for the control equation and artificial boundary conditions. It is proved that the finite difference scheme is stable and convergent with the order 2 in space and order 3/2 in time under an energy norm. A non-homogeneous numerical example demonstrates the unconditional stability and the accuracy of the algorithm.

Copyright

© 2016, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Quan Zheng
AU  - Xin Zhao
PY  - 2016/11
DA  - 2016/11
TI  - A finite difference method for heat equation in the unbounded domain
BT  - Proceedings of the 2016 International Conference on Advanced Electronic Science and Technology (AEST 2016)
PB  - Atlantis Press
SP  - 387
EP  - 392
SN  - 1951-6851
UR  - https://doi.org/10.2991/aest-16.2016.51
DO  - 10.2991/aest-16.2016.51
ID  - Zheng2016/11
ER  -