solve complex equations in MATLAB (Variable Equations)

Ali Raza

2022 2 3

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8 次查看（30 天）

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I have some equations which include some parameters and variables. Each variable defines and also exists in other equations. these are my equations:

syms Pof s Pon teta landa PIon PIof PISC
Pof = (s * y - teta + T * teta - landa + Pi * landa + alpha * p + Pon * b1 + w * b2)/(2 * b2);
s = -(y * (w - Pof))/q;
Pon = (q * s * y + 2 * w * y - 2 * w * y^2 + 2 * q * alpha + 2 * q * Pi * landa - q * teta + 3 * q * T * teta - q * landa + q * Pi * landa - q * alpha * p - 2 * y * Pof + 2 * y^2 * Pof + C * q * b1 + q * w * b2)/(2 * q * b1);
teta = (C - 3 * C * T - Pon + 3 * T * Pon)/2 * q;
landa = (-1/2) * (-1 + Pi) * (C - Pon);
Don = (1-p) * alpha - b1 * Pon + b2 * Pof - (1-y) * s + T * teta + landa * Pi;
Dof = p * alpha - b1 * Pof + b2 * Pon + y * s - (1-T) * teta - landa * (1-Pi);
PIon = (Pon-C) * Don - (1/2) * n * teta^2 - (1/2) * q * landa^2;
PIof = (Pof-w) * Dof - (1/2) * L * s^2;
PISC = PIon + PIof;

How I can solve these in order to get a numeric answer for each variable? (I don't want parametric answers)

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John D'Errico 2022-2-3

You have 10 equations, and apparently only 8 unknowns. So your problem is overdetermined. There will be no exact numerical solution.

In fact though, I can see at least a few additional variables that have no definition. Do they have values? That is, I see these:

C, T, Pi, p, b1, w, b2, y, q alpha, Don, Dof

Probably a few others that i missed. If they have no numerical values, then it is impossible to obtain ANY nunmerical solution, since you will have undetermined coefficients.

Regardless, the fact that you have 10 equations and only 8 unknowns still precludes an exact solution, unless some of those equations are effectively redundant.

Finally, could you solve that over-determined ystem using a nonlinear solver? For example, fsolve or lsqnonlin will try to minimize the residual error to the set of equations.

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