Boundary Value Problems/Lesson 7

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Boundary Value Problems

Rectangular Domain (R2)[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.

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 | edit source]

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