Integration of Numerical Solution Mathematica

[Livethefire]

I am kind of new to mathematica, and have checked the documentation but can't seem to find an answer.

I have solved 3 coupled differential equations using NDSolve.

I wish to integrate the solutions over a range but I'm not sure how to do it - the documentation seems to deal only with analytical functions. If anyone could point me in the right direction, that would be great.

(I have called my solutions "s" and was able to plot them using "/.s", I would imagine I will have to use something like this again)

 

[Dale]

If you can plot them you should be able to integrate them. Simply plot over the region you want to integrate, then replace "Plot" with "NIntegrate".

 

[Livethefire]

Thanks, Yeah I got it working.

There are curly brackets around my numerical results though :

Output: {100.00}

Anyway to get rid of them?

 

[Bill Simpson]

First[{100.00}] will give you 100.00

 

[alphy]

I can understand your frustration in trying to integrate numerical solutions in Mathematica. However, there are a few ways you can approach this problem.

Firstly, you can use the function "Integrate" in Mathematica to integrate your numerical solutions. However, this may not be the most efficient method as it requires analytical functions and your solutions may not have analytic forms.

Another option is to use the function "NIntegrate" which is specifically designed for numerical integration. This function allows you to specify the range of integration and the precision of the result. You can also use the option "Method" to choose a specific integration method that best suits your problem.

Additionally, since you have already plotted your solutions using "/.s", you can use the same syntax to integrate your solutions. For example, if you want to integrate the first solution over a range, you can use "/.s[[1]]" in the "NIntegrate" function.

I would also suggest checking out online forums and communities where Mathematica users share their experiences and solutions. You may find helpful tips and tricks from other users who have faced similar integration problems.

Overall, my advice would be to experiment with different methods and options in Mathematica and see which one gives you the most accurate and efficient results for your specific problem. Good luck!