How Does the Explicit Method Solve 1-D Heat Conduction Problems?

AI Thread Summary
The discussion centers on solving a 1-D heat conduction problem using the Explicit Method, specifically the equation U_{xx} = U_{t} with boundary conditions U(0,t) = U(1,t) = 0 and initial condition U(x,0) = sin(πx). The user is seeking hints for numerical solutions with specified parameters h = 1, k = 0.005125, and M = 200. A reference to finite difference methods is provided as a potential resource. The conversation emphasizes the need for guidance in applying the Explicit Method to this specific problem.
Lucky mkhonza
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I have been given the following problem as assignment:
Find a numerical solution for the 1-D heat conduction (using the Explicit Method):

\left\{\begin{array}U_{xx} = U_{t},\\<br /> U(x,0) = \sin \pi x, \\<br /> U(0,t) = U(1,t) = 0

Use h = 1, k = 0.005125 and M = 200.

Can anyone help by giving me a hint of this problem.

Thank you in advance...
 
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