We extend previous work on nonstandard finite difference schemes for one-space dimension, nonlinear reaction-diffusion PDEs to the case where linear advection is included. The use of a positivity condition allows the determination of a functional relation between the time and space step-sizes, and p
EXACT FINITE DIFFERENCE SCHEMES FOR TWO-DIMENSIONAL ADVECTION EQUATIONS
✍ Scribed by R.E. Mickens
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 123 KB
- Volume
- 207
- Category
- Article
- ISSN
- 0022-460X
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## Abstract A higher‐order accurate numerical scheme is developed to solve the two‐dimensional advection–diffusion equation in a staggered‐grid system. The first‐order spatial derivatives are approximated by the fourth‐order accurate finite‐difference scheme, thus all truncation errors are kept to
We construct finite difference schemes for a particular class of one-space dimension, nonlinear reactiondiffusion PDEs. The use of nonstandard finite difference methods and the imposition of a positivity condition constrain the schemes to be explicit and allow the determination of functional relatio