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I need to write and solve a set of differential equations with Mathematica, like below:

eqns[numb_] := 
 Table[{Subscript[W, i]'[
     t] == (Subscript[\[Eta], i][t] - \[Mu] - \[Sigma]^2) Subscript[W,
        i][t] + J (1 - Subscript[W, i][t]), 
   Subscript[W, i][0] == 1}, {i, 1, numb}]

I expect to find the solutions Subscript[W,i][t]. However, I struggle in the first place to write the functions Subscript[\[Eta], i][t]properly. In my model Subscript[\[Eta], i][t] represents a Gaussian random variable with a given mean m and a given variance \sigma^2. So essentially for every single function Subscript[W,i][t], the function Subscript[\[Eta], i][t] should have random values that change in time within a Gaussian distribution for example. This distribution (its mean value and variance) can be in principle different for different functions Subscript[W,i][t].

How do I do that? Is NDSolve the right tool to solve this set of equations in Mathematica?

Gabriele Stevanato
  • 31
  • 2
  • You should use an SDE solver and formulate your equation in the appropriate SDE framework, either Ito or Stratanovich. Also, you should contemplate what kind of solution you expect, as the general solution is a collection of random paths. Or said differently, each continuous function is a solution, with some equation-dependent "probability". – Lutz Lehmann Sep 03 '21 at 17:26

0 Answers0