Mathematics Stack Exchange
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Questions tagged [nonlinear-system]

In mathematics, a nonlinear system of equations is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one.

In mathematics, a nonlinear system of equations is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. Reference: Wikipedia.

In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the unknown variables or functions that appear in it (them).

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Solving a system of non-linear equations with 10 equations and 10 unknowns

I'm working on a problem where I seem to have run into a system of non-linear equations. I have ten equations and ten unknowns. In the equations below, all of the $\phi_{ij}$'s are known, but all of the $a_{1},...,e_{2}$ are…
Jeff
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Solution of system of non-linear equations

Is there a general condition for the existence and uniqueness of solution of a system of simultaneous non-linear equations similar to the determinant test for a system of linear equations. What are the solution methods (theoretical and numerical)…
Julie Kirk
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Sum of three variables given two equations

Given $$x^2+y^2+z^2=121$$ $$x\sqrt{11} + 4y + z\sqrt{22}=77$$ Find $$ \frac{\sqrt{11} + 4 + \sqrt{22}}{x+y+z} $$ I tried to plug in something for z at first, since x and y should have unique values for every value of z, but that didn't seem to…
coronermclarson
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Another proof that solutions to ẋ=f(x) can't oscillate

Let $ẋ=f(x)$ be a vector field on the line. Use the existence of a potential function $V(x)$ to show that solutions $x(t)$ cannot oscillate. I know from the textbook (Nonlinear Dynamics and Chaos, Strogatz) that there are no periodic solutions to…
liveFreeOrπHard
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3 unknown, 3 nonlinear equations of form $xy - z =$ constant

How can I solve: $$xy - z = a $$ $$xz - y = b $$ $$ yz - x = c $$ for $x, y, z$ (where $a,b,c$ are constants)? Let all variables and constants be integers (or at least rational)
doc holiday
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How do I get an analytical solution to this nonlinear equation?

Equations (3(a)-(b)) and (4(a)-(b)) from "Numerical Experiments on Application of Richardson Extrapolation With Nonuniform Grids" (DOI) provide the following solution to a nonlinear equation: My question: How do they get from (2) to (3)? To provide…
tlewis3348
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Solve three nonlinear equations in three unknown

I have the set below of three nonlinear equations: \begin{align} Y_1=&\;\frac{X_1+GX_2X_3}{1+X_2X_3} \tag1\\ Y_2=&\;\frac{X_1+GX_2X_3+GX_2(1-X_3)^2}{1+X_2X_3+X_2(1-X_3)^2} \tag2\\ Y_3=&\;\frac{X_1+GX_2X_3+FGX_2(1-X_3)^2}{1+X_2X_3+FX_2(1-X_3)^2}…
Rayan Jordan
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Sufficient conditions for the existence of the solution to the system of non-linear equations

The question of existence of the solution for an arbitrary system of non-linear equations $F(x)=0$ where $F: \mathbb{R}^{n} \rightarrow \mathbb{R}^{n}$ is undecidable (following Existence and uniqueness of solutions to a system of non-linear…
Fedor
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Very stupid question about non-linear equations.. :D

This will get me lots of negatives because I won't be able to explain myself and it is a bit of a personal quandry, but!! :p - Why are non-linear system solutions searched for using a linear numerical system? .. By linear numerical system I mean…
Ilya Grushevskiy
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Examples of nonlinear systems that cannot be modeled by multilinear systems?

In university I have learnt about the concept of tensors, which are multilinear maps in that it is a map such that it is linear with respect to all its arguments $$f(a+b+c+d+e+f+g....)=f(a)+f(b)+...+f(g)+...$$ and in physics, it is geometric in that…
Secret
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The set of elements that do not escape the tent map is a Cantor Set

Let $x \in [0,1]$ and $r>2$. Define the Tent map by $$T(x) = \left\{ \begin{array}{lr} xr & : x \in [0,\frac{1}{2}]\\ r(1-x) & : x \in (\frac{1}{2},1] \end{array} \right.$$ A point $y$ is said to escape the tent map in one…
graydad
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Degree theory and systems of nonlinear algebraic equations

For a system of nonlinear algebraic equations, how to find the number of solutions to this system? Any related degree theory can be used to determine the number of solutions? Are there any recommended references?
LCH
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"reversing" non-linear equation system

I'm not a mathematician and I'm facing a problem with those equations that I found in a book of history of colorscience. The equations were created by MacAdam to transform the classical colorimetric diagram of the CIE into something better. The CIE…
adrienlucca.net
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Equation with the variable in the exponent and also in the base

Does anyone know how to solve this equation, with the variable in the exponent and also in the base? $$1.05^{2y}-0.13y-1=0$$ Thank you very much.
Deneb
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How to invert $\max()$ and $\min()$ operators in equations

Given the following equation: $$a=\max[\min(c,gy+s),f]$$ where $a$, $c$, $y$, $s$ and $f$ are real numbers. I would like to get $y$ in closed form moving variables from the right-hand side to the left-hand side of the above equation. Is it possible…
Lisa Ann
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