Differential Equations Lecture Work Solutions 225

Differential Equations Lecture Work Solutions 225 - 1d uxx...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
1d. u xx +10 u xy +9 u yy = y A =1 B =10 C =9 4 = 100 36 = 64 hyperbolic dy dx = 10 ± 8 2 % 9 & 1 ξ = y 9 x = 9 ξ y η = y x = 1 η y u x = 9 u ξ u η u y = u ξ + u η u xx = 9( 9 u ξξ u ξη ) ( 9 u u ηη ) =81 u +18 u + u u xy = u + u ) ( u + u ) = 9 u 10 u u u = u +2 u + u u xx u u =(81 90 + 9) | {z } =0 u +(18 100+18) u +(1 10 + 9) | {z } u = y 64 u = y Substitute for y by using the transformation ξ = y 9 x 9 η y 9 x ξ 9 η = 8 y y = 9 η ξ 8 u = 9 η ξ 8 64 = ξ 512 9 η 512 u
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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.

Ask a homework question - tutors are online