Solving ODE numerically in Mathematica - 'ndnum' error?

[chipotleaway]

I'm trying to solve this ODE $R'(t)=\frac{-a}{R(t)^2}$ numerically in Mathematica (a, b are non-zero constants). Here's what I have:

NDSolve[{R'[t]==-a/R[t]^2, R[0]==b,
WhenEvent[R[t]==0, end=t; "StopIntegration"]}, R, {t,0,1}]

It's returning with

NDSolve:::ndnum : Encountered non-numerical value for a derivative at t==0.'

What does it mean there's a non-numerical value for a derivative at t=0 and how do I fix it?

 

[D H]

It means that your a and b aren't numerical. NDSolve wants numerical data.

 

[chipotleaway]

Thanks D H, I didn't notice I hadn't defined all my other constants to be a and b yet.

If it isn't too off-topic, how accurate is this method? I'm getting an answer of $t=1.2*10^{-8}$ whereas the solution I got from solving by hand (which I'm quite certain is correct) is $1.32*10^{-8}$.

 

[Bill Simpson]

Usually Mathematica calculates the accuracy and precision as it works through a problem.

Try giving your coefficients more than the default machine that is implied by a simple decimal point and see what you get. You can also click on Details & Options on the help page and look at options to have it work with greater precision in NDSolve.

 

[alphy]

The "ndnum" error in Mathematica indicates that there is a non-numerical value encountered in the derivative calculation at a particular point, in this case, t=0. This could be due to a variety of reasons, such as incorrect or missing initial conditions, incorrect syntax in the ODE, or invalid values for the constants a and b.

To fix this error, you can try double-checking your initial conditions and ensuring that all necessary variables and constants are properly defined. You can also try using the "EventLocator" option in NDSolve to help with the detection of events, such as R[t]=0, which may be causing the error. Additionally, you can try using the "WhenEvent" function to specify the stopping condition instead of using "StopIntegration" in the NDSolve command.

If the error persists, you may need to provide more information, such as the full code and any error messages, for further assistance in troubleshooting the issue.