The convex-combination formula proved in part (i) gives for every . Taking the supremum and using nonnegativity gives
(1)
This is the discrete maximum principle for the nonlinear upwind step and proves the requested conditional stability under the propagated Courant–Friedrichs–Lewy condition.

Ancestors (14)

  1. ii
  2. b
  3. 3
  4. A
  5. 2010
  6. Past exam of the numerical solution of differential equations course of the University of Oxford
  7. Numerical solution of differential equations course of the University of Oxford
  8. Year 3 of the mathematics course of the University of Oxford
  9. Mathematics course of the University of Oxford
  10. Undergraduate course of the University of Oxford
  11. Course of the University of Oxford
  12. University of Oxford
  13. List of universities
  14. Home

View article source

Discussion (0) New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version