Boundary Value Problems/Lesson 7

Boundary Value Problems

Rectangular Domain (R2) edit


Disk Domain (Polar) edit

Disc of radius c

For a disk with a radius of "c", let the polar coordinates be  , and  

  , boundary condition.

  continuity of potential.

  continuity of derivative.

  The solution as a product of two independent functions. By substitution into the above PDE we have:




The constant may be greater than , equal to or less than zero.




Use the continuity conditions and try to determine something more about A, B and λ.
  thus   and  
Either   or  
Before choosing, apply the second boundary condition:

The continuity of the derivative provides a second condition:
Either   or  
If either A or B are zero then   also must hold. So all we need is   which implies  . Remember  

Example of Potential equation on semi-annulus. edit

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