# Solving systems of nonlinear ordinary equations in Mathematica.

• Mathematica

## Main Question or Discussion Point

I'm trying to solve a system of five nonlinear equations (degree 7) in Mathematica:

Code:
Solve[{q (a^2 +
b^2 (3 q^2 + r^2 + 8 t^2)) ((e - q)^2 - R^2 - 4 T^2)^2 +
q ((e - q)^2 + R^2 + 4 T^2) - 2 (e - q) (r R + 4 t T) == 0,
R (a^2 + b^2 (3 R^2 + (e - q)^2 + 8 T^2)) ((e - q)^2 - R^2 -
4 T^2)^2 + R (R (R - r) - (e - 3 q) (e - q) + 4 T (T - 2 T)) -
r ((e - q)^2 + 4 T^2) == 0,
r (a^2 + b^2 (3 r^2 + q^2 + 8 t^2)) ((e - q)^2 - R^2 - 4 T^2)^2 -
r (R^2 + (e - q)^2 + 4 T ^2) + 2 R (q (e - q) - 4 t T) == 0,
T (a^2 + 2 b^2 (2 T^2 + (e - q)^2 + R^2)) ((e - q)^2 - R^2 -
4 T^2)^2 + T (4 T (T - t) - (e - 3 q) (e - q) + R (R - 2 r)) -
t ((e - q)^2 + R^2) == 0,
t (a^2 + 2 b^2 (2 t^2 + q^2 + r^2)) ((e - q)^2 - R^2 - 4 T^2)^2 -
t (4 T^2 + (e - q)^2 - R ^2) + 2 T (q (e - q) - rR) == 0
}, {q, r, t, R, T}]
but the program is running for an hour...
there is hope that it get to the end?

How do I have to change it to hope to arrive at the conclusion?

Thanks

## Answers and Replies

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If it isn't just a simple scrape and paste error then this worries me

) - rR) == 0

Perhaps you want a space between r and R there.

Sometimes when you have very complicated expressions you can make a simplification that can speed things up. For example, you have dozens of (e-q) in your equations. If you could substitute emq for (e-q) everywhere, patch the few isolated remaining q with (e-emq) and see whether this resulted in enough simplification then it might help speed things up.

I would also look for large common subexpressions and see whether you might be able to find a way to substantially simplify this before throwing it at Solve.

In general I would expect throwing 5 seventh order complicated multivariate polynomials at Solve to never finish in an acceptable time or with an acceptable result.

Assumptions may help as well.