EEE 431 Computational Methods in Electrodynamics

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EEE 431Computational Methods in Electrodynamics

• Lecture 5
• By
• Dr. Rasime Uyguroglu
• Rasime.uyguroglu_at_emu.edu.tr

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FINITE DIFFERENCE METHODS (cont).
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Finite Difference Method

• Solve the diffusion Equation (Parabolic D.E.)
• Subject to the boundary conditions
• And initial condition

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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 .

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Finite Difference Method

• Using explicit method
• Solve the problem for since it is
  symmetric.

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Finite Difference Method
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X t 0 0.1 0.2 0.3 0.4 0.5 0.6 1.0
0 50 100 100 100 100 100 100 50
0.005 0 75.0 100 100 100 100 100 0
0.01 0 50 87.9 100 100 100 100 0
0.015 0 43.75 75 93.75 100 100 100 0
0.02 0 37.5 68.75 87.5 96.87 100 96.87 0
0.025 0 34.37 62.5 82.81 93.75 96.87 93.75 0
0.03 0 31.25 58.59 78.21 89.84 93.75 89.84 0
. . .
1.0 0 14.16 27.92 38.39 45.18 47.44 45.18 0
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Finite Difference Method

• Implicit Method
• Choose
• The values at the fixed nodes are calculated as
  it is calculated in the implicit formulation.

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Finite Difference Method

• For the free nodes we use the formula obtained

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Finite Difference Method

• The value of for the first time step

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Finite Difference Method

• Solution of 4 simultaneous equations gives the
  values of at t0.04.
• Using these values of and applying the
  same equation, a set of simultaneous equations
  can be obtained for t0.08.