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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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Non-linear system solution via Brower degree

My aim is to prove that the system $$ \begin{cases} 2x+y+\sin (x+y) = 0 \\ x-2y + \cos (x+y)=0\end{cases}$$ has, at least, one solution in the ball $B_r(0)$ where $r>1/\sqrt{5}$. This problem is in the book Nonlinear functional Analysis (Ch. 1) by…
Senna
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System of Nonlinear algebraic equations

If we reach the tolerance function in solving a system of non - linear equations from one point to the next, can it be said that the roots obtained are not converging at these points?
anousheh
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Non linear systems of equations (Convergence).

I am an engineering student and I don't have any mathematical background in iterative methods. I am trying to solve a non-linear system of 14 equations and 14 unknowns as part of a project. I tried solving the system using both Jacobi and…
Karl Maroun
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solving a system of nonlinear equations containing logarithm

I need to solve the following system of equations analytically if it's possible, or numerically, for (x1, x2, x3, x4) : ln[x1+0.450*x2] + 1.61*x3*(1+0.200*x4) - 1.610 = 0 ln[x1+0.380*x2] + 2.30*x3*(1+0.143*x4) - 1.946 = 0 ln[x1+0.333*x2] +…
Rami Zouari
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Finding the indices of fixed points of a 2-D system

so while studying non linear dynamics I came across a simple question that I cannot find the solution to anywhere. Consider the following system: $$\begin{align} \frac{dx}{dt} &= y + y^{2} \\ \dfrac{dy}{dt}&= \dfrac{-1}{2}x +\dfrac{1}{5}y -xy +…
Robbie Meaney
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How tanh has to do with nonlinearity

I was reading an article about image processing and I came across sigmoidal activation function and tanh like in this article: But I'm struggling to understand the concept behind the nonlinearity here and what has to do with tanh, could anyone…
user474921
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Track one unique solution among all multiple solutions of a nonlinear equation system

In my engineering problem, there are about 30 variables and 30 nonlinear equations, and there can be more than 100 solutions. Only one unique solution is what I need. The following system is a simple…
YAN
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Analytic solution for high-order non-linear differential equation

Is there a way to analytically solve an equation of this form: $$y''''[x]+y[x]*y'''[x]=0$$ where the initial conditions for y through the fourth derivatives are known. I have used lower-order substitutions to convert the equation to a system of…
user3213998
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Passive input-output pair in nonlinear system

Currently, I follow a course in modeling nonlinear engineering systems, where I encountered the topic of passivity in nonlinear systems. The following dynamics were given in an exercise: $m\ddot{x} + \dot{x} + \dot{x}^7 = F$ I was asked to show that…
Thom
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$ f(a, b)\ =\ ? $; $ f(a, b) = \frac{a}{b}, a > b $; $ f(a, b) = -\frac{b}{a}, a < b $ ;$ f(a, b) = 0, a = b $

Help me find the function definition if: $$ f(a, b)\ =\ ? $$ $$ f(a, b) = \frac{a}{b}, a > b $$ $$ f(a, b) = -\frac{b}{a}, a < b $$ $$ f(a, b) = 0, a = b $$ $$ a > 0; b > 0; $$
OlegSerov
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nonlinear equations and fractions

Earlier today, i had a simple test on linear equations. since i got done early, i started fooling around, trying to calculate the equation for the tables and charts. one equation that is proving to be really difficult to solve is the seemingly…
Alexander Day
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Help me with my assignment in pre calculus about System of Non Linear Equations

System of Non Linear Equations: Solve the following using either substitution or elimination method. Verify your answer by sketching its graph $3x - 2y = 0\\ x^2 + (y - 1)^2 = 11$ $8x^2 - y^2 + 16y - 18 = 0\\ 2y^2 - 48x - 16y - 3 = 0$
user488776
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How to solve that equation containing x itself and exponential of x?

Is there a way to get the value of $x$ from $Ax - B \frac{e^{-x}}{1+e^{-x}} = C$ where A, B and C are constants?
user5054
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Help with System of nonlinear equations!

I have post once here about this question but i had some problems and i stopped with solving it. Now i started again and i think i`ve made it better. Here is where i need help. This is the system of nonlinear equations. f(x) = 0 where: $$ \left\{…
Bambus
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**Take the damped nonlinear pendulum equation $ \ \ θ′′ + μθ′ + (g/L) \ sin θ = 0 \ $ for some μ > 0 (that is, there is some friction)

Take the damped nonlinear pendulum equation $ \ \ θ′′ + μθ′ + (g/L) \ sin θ = 0 \ $ for some μ > 0 (that is, there is some friction). a) Suppose μ = 1 and $ \frac{g}{L} = 1 $ for simplicity, find and classify the critical points. b) Do the same…
MAS
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