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# EEE 431 Computational Methods in Electrodynamics - PowerPoint PPT Presentation

EEE 431 Computational Methods in Electrodynamics. Lecture 5 By Dr. Rasime Uyguroglu [email protected] 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

• Solve the diffusion Equation (Parabolic D.E.)

• Subject to the boundary conditions:

• And initial condition

• Mathematical model of a temperature distribution of 1m long rod, with its ends in contacts with ice blocks which is initially at .

• Using explicit method:

• Solve the problem for since it is symmetric.

• Implicit Method

• Choose

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

• For the free nodes we use the formula obtained :

• The value of for the first time step:

• 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.