4: Power series methods
( \newcommand{\kernel}{\mathrm{null}\,}\)
- 4.1: Power Series
- Many functions can be written in terms of a power series. If we assume that a solution of a differential equation is written as a power series, then perhaps we can use a method reminiscent of undetermined coefficients. That is, we will try to solve for the coefficients of the expansion . Before we can carry out this process, let us review some results and concepts about power series.
- 4.2: Series Solutions of Linear Second Order ODEs
- This section defines ordinary and singular points and explains how to find a power series solution around an ordinary point for differential equations.
- 4.3: Singular Points and the Method of Frobenius
- While behavior of ODEs at singular points is more complicated, certain singular points are not especially difficult to solve. Let us look at some examples before giving a general method. We may be lucky and obtain a power series solution using the method of the previous section, but in general we may have to try other things.
Contributors and Attributions
- Jiří Lebl (Oklahoma State University).These pages were supported by NSF grants DMS-0900885 and DMS-1362337.