Consider the PDE for u = u ( x , t ) utt = c 2 uxx,
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Question:
Consider the PDE for u ux t
utt c
uxx, c in R
u t uL t L in N
ux utxpi sin pi x
a Give a physical interpretation of the PDE and its boundary and initial conditions.
marks
b Write down an explicit central difference scheme to solve the PDE on the interval
making sure all terms and variables are defined consistently. You will need to
include the discrete initial conditions for your algorithm.
marks
c Write a Python script that numerically solves the PDE with the stated initial and
boundary conditions. You may use the codes from tutorials as guidance and a starting
point, if you wish. Take c
to be the last nonzero digit of your university ID number,
and take L to be the penultimate nonzero digit of your ID number. You will need to
choose suitable values for other variables. Run your script with a suitable timestep and
grid spacing. Make a two dimensional plot that shows the solution at equally spaced
moments in time. Your results should look smooth not jagged or piecewise The title
of the plot must include your ID number it will not be marked without it Your code
should include comments to aid the reader. Include a copy a screenshot or a PDF of
your code and the plot as well as uploading your code
Related Book For
Calculus For Business, Economics And The Social And Life Sciences
ISBN: 9780073532387
11th Brief Edition
Authors: Laurence Hoffmann, Gerald Bradley, David Sobecki, Michael Price
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