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hw4 - y x for x> 0 and discuss its dependence on p(the...

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MAE294B/SIO203B: Methods in Applied Mechanics Winter Quarter 2010 http://maecourses.ucsd.edu/mae294b Homework IV Due February 4, 2010. 1 The function y ( x ) satisfies the equation ˙ y + y x + ε - x ( x + ε ) 2 1 y = 0 , 0 < ε 1 . Find approximations to y ( 0 ) and to lim x y ( x ) for the two boundary conditions y ( 1 ) = 1 and y ( 1 ) = 2. 2 The function y ( x ) satisfies the equation ε y + 1 - x 2 y - y 2 = 0 , y ( - 1 ) = 1 , y ( 1 ) = 1 , 0 < ε 1 . Find two terms in the inner and outer expansions of y . 3 The function y ( x ) satisfies the equation ε y + x p y - y = 0 , y ( 0 ) = 1 , lim x y ( x ) = 0 or 1 , 0 < ε 1 . Find a uniformly valid solution for
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Unformatted text preview: y ( x ) for x > 0 and discuss its dependence on p (the boundary condition to use for large x depends on p ). 4 (Kevorkian & Cole 4.3.5) Solve the boundary-value problem y 00 + y-ε y 2 = , y ( , ε ) = , y ( ε-1 , ε ) = 1 , < ε ± 1 using (i) the method of multiple scales and (ii) boundary layer theory. Compare the two solutions. 1...
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  • Winter '08
  • Young,W
  • Boundary value problem, Boundary conditions, Boundary Layer Theory, Kevorkian, Applied Mechanics, uniformly valid solution

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