*This preview shows
pages
1–2. Sign up
to
view the full content.*

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
**Unformatted text preview: **2 ( G-H ) H + . . . + ( G-H ) H n-1 Every term has a factor G-H , and | G-H | C t p +1 by consistency. Every term has a power of G (possibly G ) which is bounded by stability. Every term has a power of H which is bounded since the continuous problem is well-posed. There are n = t/ t terms in Eq. ( ). Therefore as n , | G n-H n | t t e Kt C t p +1 = O ( t p ) The telescoping series ( ) is exactly how error accumulates in a di f erence equation. ( ) G n-H n = n j =1 G n-j ( G-H ) H j-1 H j-1 propagates the exact solution to timelevel j-1; ( G-H ) is the local truncation error going From timelevel j-1 to j ; and G n-j propagates this error Forward with the diference method to timelevel n . 2...

View
Full
Document