Timeline for Solving PDE with power series
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
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| Apr 6, 2023 at 12:19 | answer | added | Roland F | timeline score: 0 | |
| Apr 5, 2023 at 16:47 | history | became hot network question | |||
| Apr 5, 2023 at 15:55 | answer | added | Daniel Lichtblau | timeline score: 3 | |
| Apr 5, 2023 at 12:07 | history | edited | bbgodfrey |
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| Apr 5, 2023 at 12:05 | vote | accept | António Borges Santos | ||
| Apr 5, 2023 at 12:03 | answer | added | bbgodfrey | timeline score: 5 | |
| Apr 5, 2023 at 11:29 | comment | added | António Borges Santos | @RolandF this cannot be solved by DSolve. | |
| Apr 5, 2023 at 11:29 | comment | added | António Borges Santos | @bbgodfrey I see, we can assume that they are all zero. | |
| Apr 5, 2023 at 11:05 | comment | added | bbgodfrey |
This problem is ill posed. To obtain a solution, derivatives of f[0,y] to all orders must be specified for y =0.
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| Apr 5, 2023 at 10:10 | comment | added | Roland F | I dont understand the question. The ODE f' + f^2 = a + b x + c x^2 or anything else solvable by DSolve yields a solution of. Making the coefficients to be functions of y with a given derivative at y=0 can be done by substituons | |
| Apr 5, 2023 at 9:55 | history | edited | António Borges Santos | CC BY-SA 4.0 |
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| Apr 5, 2023 at 8:46 | comment | added | Syed | Welcome to the Mathematica Stack Exchange. The introductory book written by the inventor is a good learning resource. There is a fast intro for math students as well as a fast intro for programmers to choose from. | |
| Apr 5, 2023 at 4:58 | comment | added | António Borges Santos | @bbgodfrey Thanks. The issue is that Series outputs an enormous expression and manually finding f[0,0] and f[0,y]/.y by hand and removing the terms is already cumbersome (there must be a way around this). Then I also do not know how to solve for those coefficients. | |
| Apr 5, 2023 at 4:55 | comment | added | bbgodfrey | It is late here. If no one has provided an answer by tomorrow morning, I may do so. In the meantime, search this web site for similar questions. | |
| Apr 5, 2023 at 4:52 | comment | added | bbgodfrey |
The expansion I suggested will contain f[0,0] and f[0,y]/.y->0. Set them to zero. First try the expansion with a small n.
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| Apr 5, 2023 at 4:45 | comment | added | António Borges Santos | @bbgodfrey In particular, how do I implement the initial conditions? | |
| Apr 5, 2023 at 4:39 | comment | added | António Borges Santos | @bbgodfrey I am very sorry, but since I am not very familiar with Mathematica, do you think you could provide a minimal working example? | |
| Apr 5, 2023 at 4:31 | comment | added | bbgodfrey |
Use Series to expand the D[f[x,y],x]+f[x,y]^2-V[x,y]about {0, 0} and Solve for the coefficients.
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| Apr 5, 2023 at 3:53 | answer | added | Shilki Paolola | timeline score: 0 | |
| Apr 5, 2023 at 3:51 | history | edited | António Borges Santos | CC BY-SA 4.0 |
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| S Apr 5, 2023 at 3:50 | review | First questions | |||
| Apr 5, 2023 at 8:46 | |||||
| S Apr 5, 2023 at 3:50 | history | asked | António Borges Santos | CC BY-SA 4.0 |