2. Centered-difference formula for the second derivative with two independent variables r and y a?u (x, y) = и(х+h.у ) — 2и(х,у)+и(х-h-у) и (§ , y ) 12 ax4 h? a²u (x , y) = h² a+u - (1 , η ) 12 əy4 и(x.y+h) — 2u(х .у) +и(х.у-h) where { E (x – h,x + h) and 7 E (y – h, y + h).
2. Centered-difference formula for the second derivative with two independent variables r and y a?u (x, y) = и(х+h.у ) — 2и(х,у)+и(х-h-у) и (§ , y ) 12 ax4 h? a²u (x , y) = h² a+u - (1 , η ) 12 əy4 и(x.y+h) — 2u(х .у) +и(х.у-h) where { E (x – h,x + h) and 7 E (y – h, y + h).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2. Centered-difference formula for the second derivative with two independent variables r and y
a?u
(x, y) =
и(х+h.у ) — 2и(х,у)+и(х-h-у)
и
(§ , y )
12 ax4
h?
a²u
(x , y) =
h² a+u
- (1 , η )
12 əy4
и(x.y+h) — 2u(х .у) +и(х.у-h)
where { E (x – h,x + h) and 7 E (y – h, y + h).
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