Figure I shows a one-meter bar with a non-insulating side surface. Students are required to identify a suitable non-linear ODE governing equation of the system and the NEUMANN Boundary Conditions. A reference must be cited and justified for the non-linear ODE in the Project I report.
The students must decide the number of nodes to be used to discretize the domain with equal distance, where the node number starts from “0” on the left boundary. Sketch the discretization.
The students can choose either central, forward, or backward finite difference approximation of the second derivative. Rewrite the governing equation by substituting the second derivative finite difference approximation.
After applying step b) to the discretized domain, write down all the equations. d) The boundary conditions must be incorporated into the equations. e) Then, assemble the equations in the form of a matrix equation.
The matrix equation has to be solved using MATLAB, Python, or C++, and the results must be graphically presented.
The students have to record oral presentations with a duration of not more than 5 minutes. The presentation should emphasize the chosen Non-linear ODE, Neumann BC, discretized domain, formulation of finite difference equations, assembly of equations in the form of a matrix equation, line of coding, and results representation.
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