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Problem in getting detailed "stepwise results" in Wolfram Alpa Pro.

Robert Clark
Posted 8 years ago

I have a rather complicated differential equation to solve below:

{ y"(x)=.00002*EXP((3400-SQRT(3410^2+(y(x)/1000)^2))/11.1)*y'(x)^2, y(0)=1000000, y'(0)=-16000} from 50 to 70 using runge-kutta h=.5

Wolfram Alpha Pro seems to be able to solve it in that it gives the abbreviated "stepwise results" table. But when I click the "More" link to get the detailed data, it just runs and runs without delivering the data.

Any idea what the problem is?

Bob Clark
POSTED BY: Robert Clark
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Updating Name
Posted 8 years ago

I now made two changes in the way I input the equation on the chance that the large numbers involved were taking a long time to do the calculations, and this time it worked to display the detailed data.

I first changed the units involved for y from meters to kilometers so the initial data was y(0)=1000, y'(0)=-16. Also for the fraction in the exponent of the EXP function I divided top and bottom by 1,000 so smaller numbers would have to be calculated up in the exponent.

The new way I input the equation is here (the change to a .02 in front was due to the change in units):

{ y"(x)=.02EXP((3.4-SQRT(3.41^2+(y(x)/1000)^2))/.0111)y'(x)^2, y(0)=1000, y'(0)=-16} from 50 to 70 using runge-kutta h=.25

I'm going to trying now making the step number smaller to h=.1 to get more accurate solution and see if I can still get the more detailed answer.

BTW, I need to know y' as well as y in the solution. Is there a way to get Wolfram Alpha to do this?

Bob Clark
POSTED BY: Updating Name
Robert Clark
Robert Clark
Posted 8 years ago

Thanks for the response. I do have Mathematica at work, but I'm on Summer break until July. Thanks also for the Mathematica input syntax for the problem. I'll copy this directly into Mathematica when I use it at work.

About the "data" button, it only allows you to download the results now showing on screen. So if it is only the abbreviated table showing, then that is what you can download by hitting the "data" button.

Did you have the same problem I had when running this in Wolfram Alpha Pro?

Bob Clark
POSTED BY: Robert Clark

Yes, I did have the same issue, but I don't have the Pro version. However, I would also not use WolframAlpha for this... Mathematica seems a better, more 'controlled' way of tackling the problem...
POSTED BY: Sander Huisman

Hi Robert,

If you have access to Mathematica you can easily get all points:

RK4Coefficients[4,p_]:=N[{{{1/2},{0,1/2},{0,0,1}},{1/6,1/3,1/3,1/6},{1/2,1/2,1}},p]
ifun=y/.NDSolve[{y''[x]==0.00002 E^(0.0900901 (3400-Sqrt[11628100+y[x]^2/1000000])) y'[x]^2,y[0]==1000000,y'[0]==-16000},y,{x,0,70},Method->{"FixedStep",Method->{"ExplicitRungeKutta","DifferenceOrder"->4,"Coefficients"->RK4Coefficients}},StartingStepSize->0.5,WorkingPrecision->MachinePrecision][[1]];
Transpose[{ifun["Grid"]//Flatten,ifun["ValuesOnGrid"]}]

Have you tried clicking the data button? does that work?

enter image description here
POSTED BY: Sander Huisman
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