Timeline for Solving an ODE in power series
Current License: CC BY-SA 3.0
7 events
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| Aug 23, 2020 at 3:25 | comment | added | A little mouse on the pampas |
This's a great answer, but I don't know why we can't compute the following differential equation case:ode = x[t]*x''[t] - 1 - x'[t]^2 == 0; initconds = {x[0] == 1, x'[0] == 0};.
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| Sep 17, 2014 at 12:23 | history | edited | Michael E2 | CC BY-SA 3.0 |
Improved formatting
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| May 19, 2013 at 15:25 | comment | added | rick | My equation has the term sin (2y(x)) so it is far from linear. When looking at the documentation for NDSolve I did not see see where one might specify the integration method to use-I was searching for a Taylor series option. | |
| May 18, 2013 at 15:03 | comment | added | J. M.'s missing motivation♦ | @rick, that's a bit unclear; is the thing inside the sine the dependent or independent variable? | |
| May 18, 2013 at 2:02 | comment | added | rick | Thank you for your answer; it is very clear. My equation is very similar to the one you use; its nonlinear term is of the form sin(2f). I am more familiar with Maple which has the basic command dsolve(equation, series) and I was sure that MMA must have such a command also. | |
| May 17, 2013 at 18:07 | comment | added | whuber | +1 This is a good start. Power series solutions, though, are frequently used to obtain recursion equations for the coefficients (of any solution that might be analytic within a neighborhood of the point of expansion). It would be nice, then, to have a function that outputs these equations (given a differential operator as input), rather than just obtaining an approximate solution with a limited radius of accuracy. In order to analyze singular points, it would also be useful to consider slightly more general series of the form $z^\alpha(a_0+a_1z+a_2z^2+\cdots)$ for non-integral $\alpha$. | |
| May 17, 2013 at 15:52 | history | answered | Daniel Lichtblau | CC BY-SA 3.0 |