0.4 Singular Boundary Value Problems

0.4 Singular Boundary Value Problems

• The differential equation is subject to these conditions.

• There are two ways in which a boundary value problem can be singular.
• A singular point of the differential equation is the endpoint of the interval of interest.
• The interval is long in the other.

• A regular singular point is 0 Section 1 of the equation has a regular singular point at the origin.

• A boundary point is a mathematical boundary without being a physical boundary.
• The mathematical boundary is in the interior of the disk.

• We enforce the condition explicitly when a singular point is a boundary point.
• In the example that follows, we will see how these conditions act to make the solution of a boundary value problem unique.

• Only the physical boundary condition has been noted.

• The differential equation is easy to solve.

• An ordinary boundary condition works at an ordinary point.
• The second boundary condition determines 2.

• The interval of interest is infinite in a singular boundary value problem.
• No boundary condition is imposed at the other end.

• Add the appropriateBoundedness condition to solve the problem.

• Provide and solve the properBoundedness condition.

• The boundary of the sphere has a 0.
• Section 0.1 is called Exercise 19.