Undergrad Using D'Alembert Solution to Find Values of Regions

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The discussion focuses on using D'Alembert's solution to determine the values of regions in a grid, particularly emphasizing that regions containing specific points (like x = 0 and x = 4) should have a value of 0. Participants explore how boundary conditions can influence the bottom values of the grid. There is also a query regarding the appearance of the initial condition when applied to a problem on the real line. Understanding D'Alembert's solution and the time derivative at t=0 is crucial for interpreting the figure presented. Overall, the conversation centers on the mathematical principles underlying the solution and its implications for the grid values.
FAS1998
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How were the values of the the regions found in the grid of this solution? I understand that the value should be 0 in every regions that contains the points x = 0, x=4, etc...

I believe the bottom values can be found from the boundary conditions as well, but what about the others?
 
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Do you understand why the initial condition looks the way it does when extended to a problem on the real line?

Once you have that and d’Alembert’s solution for the time derivative at t=0 being equal to zero you should be able to understand the figure.
 
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