Posted: November 1st, 2022

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Hello,

Please answer the following exercise as per given instructions

Instruction:

If you were caught copying program or code from online source, you will receive

zero score for this project.

Project Prompt:

Solve the wave equation

0

u u

t x

+ =

using

i.

First order upwind scheme

ii. MacCormack scheme

for the initial conditions

u x( ,0) 1 = x 10

u x( ,0) 0 = x 10

and Dirichlet boundary conditions.

Choose a 41-grid point mesh with

=x 1

and

compute to t=18. Solve this project for

= 1.0, 0.6, and 0.3.

Each student has to submit the following items to Canvas portal to receive full credits:

a. Tabulated results of u for exact and numerical solutions at t=18 (2 points)

b. Graphs for comparison between exact and numerical solutions (4 points)

c. An electronic MATLAB file for my code execution. (4 point

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