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EEE 431 Computational Methods in Electrodynamics. Lecture 5 By Dr. Rasime Uyguroglu Rasime.uyguroglu@emu.edu.tr. FINITE DIFFERENCE METHODS (cont). Finite Difference Method. Solve the diffusion Equation (Parabolic D.E.) Subject to the boundary conditions: And initial condition.
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EEE 431Computational Methods in Electrodynamics Lecture 5 By Dr. Rasime Uyguroglu Rasime.uyguroglu@emu.edu.tr
Finite Difference Method • Solve the diffusion Equation (Parabolic D.E.) • Subject to the boundary conditions: • And initial condition
Finite Difference Method • Mathematical model of a temperature distribution of 1m long rod, with its ends in contacts with ice blocks which is initially at .
Finite Difference Method • Using explicit method: • Solve the problem for since it is symmetric.
Finite Difference Method • Implicit Method • Choose • The values at the fixed nodes are calculated as it is calculated in the implicit formulation.
Finite Difference Method • For the free nodes we use the formula obtained :
Finite Difference Method • The value of for the first time step:
Finite Difference Method • Solution of 4 simultaneous equations gives the values of at t=0.04. • Using these values of and applying the same equation, a set of simultaneous equations can be obtained for t=0.08.