{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

chapter9b - Tridiagonal Sytems Silvana Ilie MTH510...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Tridiagonal Sytems Silvana Ilie MTH510 – Numerical Analysis Department of Mathematics, Ryerson University Tridiagonal Sytems – p. 1/6
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Example Thin rod between two walls heated at constant temperature The temperature satisfies d 2 T dx 2 + h ( T a T ) = 0 T – temperature; x – distance along rod h – heat transfer coefficient between rod and surrounding air T a –air temperature Tridiagonal Sytems – p. 2/6
Background image of page 2
Example (cont’d) Given boundary value conditions: T (0) = 40 ,T (10) = 200 T a = 20 h = 0 . 01 Compute Δ x = x i +1 x i = 10 5 = 2 , for i = 0 .. 4 approximate d 2 T dx 2 T i +1 2 T i + T i 1 Δ x 2 substitute in differential equation T i +1 2 T i + T i 1 Δ x 2 + h ( T a T i ) = 0 ⇒− T i 1 + (2 + h Δ x 2 ) T i T i +1 = h Δ x 2 T a Tridiagonal Sytems – p. 3/6
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Example (cont’d) Substitute T 0 = 40 ,T 5 = 200 ,h = 0 . 01 , we get T 0 + 2 . 04 T 1 T 2 = 0 . 8 T 1 + 2 . 04 T 2 T 3 = 0 . 8 T 2 + 2 . 04 T 3 T 4 = 0 . 8 T 3 + 2 . 04 T 4 T 5 = 0 . 8
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}