Boundary Value Problems/Lesson 7

From Wikiversity
Jump to navigation Jump to search

Boundary Value Problems

Rectangular Domain ()[edit | edit source]

Disk Domain (Polar)[edit | edit source]

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.

[edit | edit source]

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



Separate,




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:
thus



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 | edit source]

%%(php) <?php echo "Hello, World!"; ?> %%



Return to Main Page Boundary Value Problems