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chapter9b

# chapter9b - Tridiagonal Sytems Silvana Ilie MTH510...

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Tridiagonal Sytems Silvana Ilie MTH510 – Numerical Analysis Department of Mathematics, Ryerson University Tridiagonal Sytems – p. 1/6

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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
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

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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
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