Timeline for Using Darboux's to solve 2D system of first order linear PDEs with variable coefficients
Current License: CC BY-SA 4.0
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| Apr 26, 2022 at 17:20 | comment | added | Leif Ericson | Great, that makes sense. Last thing, I'm new to solving systems of PDEs, can you recommend a good reference discussing Darboux Method as you've invoked it here? The document I had linked in the original post seems to be a variant of the method you are talking about. Thanks again for all the help, I really appreciate it. | |
| Apr 25, 2022 at 18:43 | comment | added | Robert Bryant | @LeifEricson: What I actually meant was that, if $(h_1(t),h_2(t))$ solves the ODE system then the functions $v_i(t,x) = u_i(t,x)-h_i(t)\,\mathrm{e}^{Ax}$ will satisfy the original system with the $C_i$ set to zero, so you might as well assume that $C_1=C_2=0$. Yes, I mean $F_i$ is an anti-derivative of $f_i$. | |
| Apr 25, 2022 at 17:33 | comment | added | Leif Ericson | Thanks a lot for the reply. A few clarifying questions though. First what do you mean by "subtracting a particular solution" of the ODE system from the general solution? Do you mean that if $h_{1,p}\left(t\right)$ and $h_{2,p}\left(t\right)$ satisfy the inhomegenous system that subtracting that system from the original one gives a homogenous system in the variables $h_{i}\left(t\right)-h_{i,p}\left(t\right)$? Also, when you define $F_i'=f_i$ I take that to mean the capital F is the integrated form of the lowercase f? Thanks again for the help! | |
| Apr 23, 2022 at 19:52 | history | answered | Robert Bryant | CC BY-SA 4.0 |