Timeline for Can an integral equation always be rewritten as a differential equation?
Current License: CC BY-SA 2.5
16 events
| when toggle format | what | by | license | comment | |
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| Jan 10, 2017 at 19:58 | answer | added | Denis Serre | timeline score: 4 | |
| S May 23, 2015 at 14:35 | history | suggested | Ali Taghavi |
I add a tag
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| May 23, 2015 at 13:42 | review | Suggested edits | |||
| S May 23, 2015 at 14:35 | |||||
| Oct 8, 2010 at 8:24 | vote | accept | Michael Bächtold | ||
| Jun 11, 2010 at 9:17 | comment | added | Michael Bächtold | I'm just asking out of curiosity since I know better what PDEs are and wondered if one may consider integral equations from the same perspective. It's not that I need to apply such a procedure to a concrete equation at the moment. | |
| Jun 1, 2010 at 14:52 | answer | added | Willie Wong | timeline score: 17 | |
| Jun 1, 2010 at 13:16 | answer | added | SandeepJ | timeline score: 4 | |
| Jun 1, 2010 at 13:05 | answer | added | vonjd | timeline score: 3 | |
| Jun 1, 2010 at 12:23 | answer | added | mathphysicist | timeline score: 10 | |
| Jun 1, 2010 at 11:44 | comment | added | Deane Yang | The term "integral equation" is perhaps too vague. Any chance you want to indicate the most general form you need? Also, any chance you want to say a little about why you would want to do this. In general, we prefer to convert differential equations into integral equations and not vice versa. | |
| Jun 1, 2010 at 11:19 | comment | added | Michael Bächtold | @ Guy and Peter: sorry I fail to see how this is related to the question. | |
| Jun 1, 2010 at 11:18 | history | edited | Michael Bächtold | CC BY-SA 2.5 |
added some explanations
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| Jun 1, 2010 at 10:47 | comment | added | Peter LeFanu Lumsdaine | Indeed, taking Guy's example further towards absurdum, any function f(x) is the unique solution of the equation y(x) = f(x)! The question becomes interesting once you choose some restrictions on the coefficients involved (and perhaps other aspects of the form of the equations). @Michael: can you give some examples that you had in mind? | |
| Jun 1, 2010 at 10:39 | comment | added | Guy Katriel | Any smooth function is the solution of a differential equation: given f(x), we have that f(x) is the solution of the equation y'(x)=f'(x) for y(x) | |
| Jun 1, 2010 at 10:37 | comment | added | Charles Matthews | It might be more reasonable to ask this in a more definite context, such as Fredholm theory. The operators considered in the abstract theory of integral equations, for a given class of kernels, are very different in nature from differential operators. But the two theories are related, in some cases, by a type of inversion. You may be asking the question "how extensive is that relationship"? | |
| Jun 1, 2010 at 10:20 | history | asked | Michael Bächtold | CC BY-SA 2.5 |