Regular Singular Points A regular singular point of a differential equation is a point where the derivative is equal to zero but the function itself is n...
A regular singular point of a differential equation is a point where the derivative is equal to zero but the function itself is not zero. This means that there is a removable discontinuity at that point, and the behavior of the solution is not determined by the initial condition.
Regular singular points can be either isolated (when the solution exists only in a single interval) or regular (when the solution exists for all real values).
Examples:
For the differential equation the point is an isolated regular singular point.
For the differential equation the point is a regular singular point with a behavior that is determined by the initial condition.
For the differential equation the point is an isolated regular singular point.
Regular singular points can be treated using various methods, including Fourier series, ** Laplace transforms**, and singular value decomposition. These methods allow us to analyze the behavior of solutions near these points and determine their long-term behavior