# Coupled partial differential equations **URL:** \ **Category:** General Discussion\ **Created:** [October 9, 2019, 8:15am UTC](https://community.freefem.org/t/coupled-partial-differential-equations/150 "2019-10-09T08:15:07Z")\ **Posts on this page:** 9\ **Page:** 1
**Author:** ![reinoud](https://avatars.discourse-cdn.com/v4/letter/r/c37758/32.png) [@reinoud](https://community.freefem.org/u/reinoud)\ **Post date:** [October 9, 2019, 8:15am UTC](https://community.freefem.org/t/coupled-partial-differential-equations/150/1 "2019-10-09T08:15:07Z")
I have 5 coupled partial differential equations in t and r ( second order). Is therre someone who can help me to implement these equations in FreeFem? I am new in FreeFem and used Mathematica. ---
**Author:** ![frederichecht](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/frederichecht/32/15_2.png) [@frederichecht](https://community.freefem.org/u/frederichecht)\ **Post date:** [October 9, 2019, 9:11am UTC](https://community.freefem.org/t/coupled-partial-differential-equations/150/2 "2019-10-09T09:11:40Z")
We need the equations more less to help you, and to know if is possible solve it with freefem++ ---
**Author:** ![reinoud](https://avatars.discourse-cdn.com/v4/letter/r/c37758/32.png) [@reinoud](https://community.freefem.org/u/reinoud)\ **Post date:** [October 9, 2019, 9:56am UTC](https://community.freefem.org/t/coupled-partial-differential-equations/150/3 "2019-10-09T09:56:59Z")
Dear Frederic, Thanks for your reaction. I attached the equations I also attached the mathematica file. Hope you have suggestions. Best regards Reinoud (Attachment PDEs slagter.docx is missing) (Attachment spinn CS Mondi Marder t-dep-A.nb is missing) ---
**Author:** ![reinoud](https://avatars.discourse-cdn.com/v4/letter/r/c37758/32.png) [@reinoud](https://community.freefem.org/u/reinoud)\ **Post date:** [October 9, 2019, 10:01am UTC](https://community.freefem.org/t/coupled-partial-differential-equations/150/4 "2019-10-09T10:01:40Z")
Dear Frederic, Thanks for your reply. I send you my equations and also the Mathematica file. Hopr you can help Best regards Reinoud [slagter.zip](https://community.freefem.org/uploads/short-url/4ovHzRkZ2LyTsVG1Px562DO7Zvy.zip) (1.15 MB) ---
**Author:** ![frederichecht](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/frederichecht/32/15_2.png) [@frederichecht](https://community.freefem.org/u/frederichecht)\ **Post date:** [October 9, 2019, 10:20am UTC](https://community.freefem.org/t/coupled-partial-differential-equations/150/5 "2019-10-09T10:20:50Z")
Real, I do not, your equation are complex ,and fully no linear, You can try but it is not easy. ---
**Author:** ![frederichecht](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/frederichecht/32/15_2.png) [@frederichecht](https://community.freefem.org/u/frederichecht)\ **Post date:** [October 9, 2019, 5:27pm UTC](https://community.freefem.org/t/coupled-partial-differential-equations/150/6 "2019-10-09T17:27:21Z")
I think your equation come format quantum mechanics. If you need help, do you have a papier to explain how this equations are build, because it is a really no standard equation. for a mathematician. you can send directly the mail to [frederic.hecht@sorbonne-universite.fr](mailto:frederic.hecht@sorbonne-universite.fr) best regard. ---
**Author:** ![reinoud](https://avatars.discourse-cdn.com/v4/letter/r/c37758/32.png) [@reinoud](https://community.freefem.org/u/reinoud)\ **Post date:** [October 9, 2019, 7:53pm UTC](https://community.freefem.org/t/coupled-partial-differential-equations/150/7 "2019-10-09T19:53:09Z")
Dear Frederic, Thanks for your reply. Indeed, these equations originate from my research on cosmic strings. The 3 PDE’s for the metric ( in general relativity, mu,xi and J) are the problem. They are extracted from the Einstein equations, but the system is overdetermined, so I can write the 3 PDE’s in different form, i.e., for example such that they become parabolic. For example with diff(J,t,t) = diff(J,r,r) … The 5 PDE’s I send you is one possible isolation of the equations for mu, xi and J. The 2 PDE’s forthe matter field, X and P are fixed. I send you the maple 18 file, where you can read off the Einstein equations for mu,xi and J (Attachment Slagter-2.docx is missing) ---
**Author:** ![reinoud](https://avatars.discourse-cdn.com/v4/letter/r/c37758/32.png) [@reinoud](https://community.freefem.org/u/reinoud)\ **Post date:** [October 9, 2019, 8:04pm UTC](https://community.freefem.org/t/coupled-partial-differential-equations/150/8 "2019-10-09T20:04:38Z")
Dear Frederic, Thanks for your reply. Indeed, these equations originate from my research on cosmic strings. The 3 PDE’s for the metric ( in general relativity, mu,xi and J) are the problem. They are extracted from the Einstein equations, but the system is overdetermined, so I can write the 3 PDE’s in different form, i.e., for example such that they become parabolic. For example with diff(J,t,t) = diff(J,r,r) … The 5 PDE’s I send you is one possible isolation of the equations for mu, xi and J. The 2 PDE’s for the matter field, X and P are fixed. I send you the maple 18 file, where you can read off the Einstein equations for mu,xi and J Best regards Reinoud [slagter2.zip](https://community.freefem.org/uploads/short-url/mjZ70e4IB6D7sQ2GXeJowN21iT0.zip) (2.1 MB) ---
**Author:** ![frederichecht](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/frederichecht/32/15_2.png) [@frederichecht](https://community.freefem.org/u/frederichecht)\ **Post date:** [October 10, 2019, 12:51pm UTC](https://community.freefem.org/t/coupled-partial-differential-equations/150/9 "2019-10-10T12:51:54Z")
Dear Reinoud; I have no real idea to solve numerical you pdf. Bien cordialement, Frédéric Hecht.