{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

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

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
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

• Winter '08
• Young,W
• Boundary value problem, Boundary conditions, Boundary Layer Theory, Kevorkian, Applied Mechanics, uniformly valid solution

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern