View the step-by-step solution to:

Question

123.pngplease help me solve this problem. Thanks!

123.png

Problem 4: Consider an infinite slab of unit width. The differential equation describing the
system 15 +
0 =
d'T
= 0
=0
dz
-0
=-1
+
g(=) =10-20=
1) Using 4 eigenfunctions o(=) = H, cos(@;=), where @; = (i-1)x, H1=1, Hi = 12, i=
2...4, approximate the differential equation with a set of algebraic equations using the
Galerkin method. Report your answer in the form of Ax = b by identifying x, A and b
and indicating how an approximation of (z) can be constructed from x. You should
find the following identity useful+
=cos(@ =)d= = co
cos(@ =) = sin( ()=)
2) Show that the solution to the system of equations from part 1 is +
+
T ( = ) = a + ( b, / 1 ) ( = ) + (b; / 4. )$ (=)+(b, 195 ) (=)+
where by are element of the vector b and of is any arbitrary number. Using MATLAB,
plot 7(z) with a = 303.+
3) Repeat part 1 with g(=) =10 and show that the resulting set of algebraic equations has
no solution. Discuss this conclusion in the context of Example 2.13 from the book
(Graham and Rawlings).

Recently Asked Questions

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question
Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes