Eee 431 computational methods in electrodynamics
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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 431 computational methods in electrodynamics

EEE 431Computational Methods in Electrodynamics

Lecture 5

By

Dr. Rasime Uyguroglu

[email protected]



Finite difference method
Finite Difference Method

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

  • Subject to the boundary conditions:

  • And initial condition


Finite difference method1
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 method2
Finite Difference Method

  • Using explicit method:

  • Solve the problem for since it is symmetric.



Finite difference method4
Finite Difference Method

  • Implicit Method

  • Choose

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


Finite difference method5
Finite Difference Method

  • For the free nodes we use the formula obtained :


Finite difference method6
Finite Difference Method

  • The value of for the first time step:


Finite difference method7
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.


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