What is the most general method of approximating arbitrary systems of ODEs of 4 variables(x,y,z,t) that fit these conditions? The conditions that are assumed true of the ODEs are:(adsbygoogle = window.adsbygoogle || []).push({});

1) that I require differentials to be explicitly defined (but they can be defined in terms of other differentials).

2) that time is assumed linear (ei, it's a 3 variable system described in terms of 4, but the 4th is known)

That is:

dx=y^2+sin(x)

dy=-dz+y*t

dz=t*z

would be valid, because dx,dy, and dz are explicitly defined and alone on one side.

dx=f(dx)

would be invalid, because I don't want to solve implicit equations.

f(dx,x,y,z,t) = g(x,y,z,t)

would be invalid, because I don't want to have to move all the junk to the other side to get an explicit definition of dx.

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# Numerical Approximation of a 4D System of ODE's

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