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I would like to know if it is possible to solve differential equations and run them directly in either ArcMap or ERDAS Imagine, similar to the raster calculator in ArcMap?

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ArcGIS does solve certain kinds of differential equations related to hydrological flow. What differential equations do you have in mind? –  whuber Jan 2 at 15:40
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There is nothing built into the software that can solve differential equations. I am assuming that your values are derived from spatial data or you would be posting this on another site. Your best bet (if you are tied to one of these software packages) is to write some code in ArcPy that pulls in your values and does the math.

The NumPy Python library, which has been installed with ArcGIS since 9.2, will help you immensely, and Esri has some documentation on using it here.

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Thanks kas, what I am trying to do is to use a polygon layer which has a field which would be in my model as a variable. Now I have Matlab but I am just trying to find the best and quickest method to do it as I'm not a programmer. Otherwise would you have any ideas how to import that data into mat lab and execute a variable which is stored elsewhere and have the output from the 'runned' model into another file that can be imported and added another field next to the ones I used as variable? Thank you. J –  Jay Reynolds Apr 10 '13 at 1:43
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If you can do your diff eq work in MATLAB I would get your polygon table into a .csv (e.g. open the .dbf in a spreadsheet program and save as a .csv) then use csvread in MATLAB to read in the data you need. Do your work in MATLAB. If you need to append the predicted values (or something else) onto the original polygon data, use csvwrite to write the data back to .csv. You can open the .csv in your GIS of choice and do a simple table join with the original data (e.g. in ArcGIS 10.1 right-click your layer JOINS AND RELATES > JOINS...). I hope that helps. Let me know if you need clarification. –  TankofVines Apr 10 '13 at 2:24
    
Yeah that make sense I'll do that. Thank you Kas for your help! J –  user17005 Apr 10 '13 at 3:50
    
@JayReynolds If you get a chance it would be good if you can reward kas673 by clicking the big green tick next to his/her Answer to Accept it. –  PolyGeo Jan 2 at 7:25
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