Universität des Saarlandes
Fachrichtung 6.1 – Mathematik
PD Dr. Darya Apushkinskaya
PDE and Boundary-Value Problems (Winter Term 2014/2015)
Assignment H5 - Homework
Problem 5.1 (Solving IBVP - 6 Points)
Solve the semi-infinite string problem:
0 < x < ∞,
PDE: utt = uxx ,
0<t<∞
BC: u(0, t) = 0,
(
ICs:
0<t<∞
2
u(x, 0) = xe−x
,
ut (x, 0) = 0
0<x<∞
Problem 5.2 (Solving the IBVP - 6 Points)
Find the solution to the following vibrating-string problem
PDE: utt = α2 uxx ,
(
BCs:
(
ICs:
0 < x < L,
u(0, t) = 0
,
u(L, t) = 0
0<t<∞
u(x, 0) = sin (πx/L) + 0, 5 sin (3πx/L)
,
ut (x, 0) = 0
06x6L
0<t<∞
Problem 5.3 (The Vibrating Beam - 7 Points)
What is the solution to the simply supported (at both ends) beam problem with ICs
u(x, 0) = sin (πx)
ut (x, 0) = sin (πx)
06x61
Deadline for submission: Monday, January 12, 12pm