Computing with large vectors and matrices

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I'm working on a project that requires the use of large data sets; vectors and matrices with millions of entries. Normally I've done my projects (small scale stuff) with Matlab and never had an issue. But now I'm running into max array size issues on all the computers I've tried.

I've thought about simply storing the data in separate vectors. For instance if I want to work with a million entry vector I could store it in several vectors of length 20,000. That seems like a poor way to do it. Would switching to another language like C++ allow me to store more data in each array? Or is there a simpler and better option?

Any advice would be appreciated. Note that the project in question involves using RK4 and a fourth order Simpson's Rule on a system of differential equations (Lorenz System). And note that the only other language I have some experience with is C++. Thank you.