# EEE 431 Computational Methods in Electrodynamics - PowerPoint PPT Presentation

1 / 11

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

EEE 431 Computational Methods in Electrodynamics

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## 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.