- #1
yhasky
- 2
- 0
Hello,
I need help in solving the problem:
" find the lowest order uniform approximation to the boundary value problem εy''+y'sinx+ysin(2x)=0. y(0)=(pi), y(pi)=0. "
what I did:
y(out)=Ʃ(ε^n)y(n)
εy''(out)+y'(out)*sinx+y(out)*sin(2x)=0
for order 0: y'(out)*sinx+y(out)*sin(2x)=0
with the B.C y(pi)=0---> y(out)=0.
for the inner region:
x=εX
y(x)=Y(in)(X)
Y(in)=Ʃ(ε^n)Y(n)
Y''(in)+Y'(in)*sin(εX)+Y(in)*sin(2εX)=0
sin(εX)≈εX+ O(ε^3)
for order 0: Y''(in)=0
Y(in)=AX+B
with the B.C Y(0)=pi---> Y(out)=AX+(pi).
the matching:
x=δz, X=x/ε
ε-->0
Y(in)=A*δz/ε+(pi) -->∞
y(out)=0.
can't do the matching and find B!
Where is my mistake?
Thank you very much!
I need help in solving the problem:
" find the lowest order uniform approximation to the boundary value problem εy''+y'sinx+ysin(2x)=0. y(0)=(pi), y(pi)=0. "
what I did:
y(out)=Ʃ(ε^n)y(n)
εy''(out)+y'(out)*sinx+y(out)*sin(2x)=0
for order 0: y'(out)*sinx+y(out)*sin(2x)=0
with the B.C y(pi)=0---> y(out)=0.
for the inner region:
x=εX
y(x)=Y(in)(X)
Y(in)=Ʃ(ε^n)Y(n)
Y''(in)+Y'(in)*sin(εX)+Y(in)*sin(2εX)=0
sin(εX)≈εX+ O(ε^3)
for order 0: Y''(in)=0
Y(in)=AX+B
with the B.C Y(0)=pi---> Y(out)=AX+(pi).
the matching:
x=δz, X=x/ε
ε-->0
Y(in)=A*δz/ε+(pi) -->∞
y(out)=0.
can't do the matching and find B!
Where is my mistake?
Thank you very much!