Differential Equations Lecture Work Solutions 228

Differential Equations Lecture Work Solutions 228 - 2b....

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2b. 3 u xx +7 u xy +2 u yy + u y + u =0 A =3 B =7 C =2 4 =49 24 = 25 hyperbolic dy dx = 7 ± 5 6 % 2 & 1 3 ξ = y 2 x = 2 ξ y =1 η = y 1 3 x = 1 3 η y u x = 2 u ξ 1 3 u η u y = u ξ + u η u xx = 2 2 u ξξ 1 3 u ξη ± 1 3 2 u 1 3 u ηη ± u xx =4 u + 4 3 u + 1 9 u u xy = 2( u + u ) 1 3 ( u + u ) u xy = 2 u 7 3 u 1 3 u u = u u + u 4 u 49 3 u +4 u + u ξ + u η + u 25 3 u + u ξ + u η + u Use last page: 25 3 ( U + βU ξ + αU η + αβU )+ U ξ + + U η + + U 25 3 U + 25 3 β +1 ± U ξ + 25 3 α ± U η + 25 3 αβ + α + β ± U ⇓⇓ β / 25 α / 25 3 25 + 3 25 + 3 25 +1= 28 25
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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