Abstract
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.
Original language | English |
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Pages (from-to) | 261-277 |
Number of pages | 17 |
Journal | Applied Numerical Mathematics |
Volume | 50 |
Issue number | 2 |
Early online date | 12 Feb 2004 |
DOIs | |
Publication status | Published - Aug 2004 |
Scopus Subject Areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics
User-Defined Keywords
- Artificial boundary condition
- Finite difference
- Heat equation
- Unbounded domain