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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Non-linear system of 2 equal differential equations

I am trying to solve a nonlinear system of differential equations: $a\ddot{x} = -\frac{b}{\sqrt{\dot{x}^2 + \dot{y}^2}}\dot{x}$ $a\ddot{y} = -\frac{b}{\sqrt{\dot{x}^2 + \dot{y}^2}}\dot{y}$ The fact that both equations for $x$ and $y$ are the same…
Sergio García
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Barbalat's lemma for Stability Analysis

Good day, We have: Lyapunov-Like Lemma: If a scaler function V(t, x) satisfies the following conditions: $V(t,x)$ is lower bounded $\dot{V}(t,x)$ is negative semi-definite $\dot{V}(t,x)$ is uniformly continuous in time then $\dot{V}(t,x) \to 0$ as…
Pietair
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System of 3 simultaneous equation where one is non-linear

Hi I have a problem where I need to solve the following set of equations: $$ v = U u $$ $$ u = 1 -Uv $$ $$ U^2 = u^2 + v^2 $$ I have tried subbing $u$ and $v$ into the expression for $U^2$ but it seems to get very messy very quickly. Any help…
Will Watson
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3x3 non-linear system of equations (Known and unkown isotope decay)

TLDR version: is it possible to solve the following system for X, Y, Z? $C_1=X+Y$ $C_2=C_3 X + Y Z^{C_4} $ $C_5=C_6 X + Y Z^{C_7} $ Background/Context: I have a mixture with a known isotope A (known decay constant $λ_Α$) and an unknown one B…
aggelosv
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Solving the IBVP $u_t+uu_x=Du_{xx}$ using Crank Nicolson implicit scheme

I am solving the IBVP $u_t+uu_x=Du_{xx}$ using Crank Nicolson implicit scheme, with periodic boundary conditions. Discretization leads to a system of type $Au^{n+1}=Bu^n+F(u^{n+1})$, where $A$ and $B$ are variable matrices and $F$ is a nonlinear…
Bibigul
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Properties of nonlinear equation system

Considering the very simple electrical dc power flow problem with two nodes, with voltage V1 and V2 respectively, connected via a resistance R, we end up with a system of two nonlinear equations: $P_1=\frac{V_1(V_1-V_2)}{R}$…
SuperGeo
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How can you tell whether the equation of a non-linear relationship represents a parabola, a hyperbola or a circle?

How can you tell whether the equation of a non-linear relationship represents a parabola, a hyperbola or a circle?
odette
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$4$ variable system of equations

Find all the solutions to this system of equations: $$\begin{cases} -2d^3+3a^2d+d+2c^3-3a^2c-c=0\\ 2d^3-3db^2-d-2c^3+3b^2c+c=0\\ -6c^2b+b^3+b+6c^2a-a^3-a=0\\ 6d^2b-b^3-b-6d^2a+a^3+a=0 \end{cases}$$ After factoring: $$\begin{cases}…
Rasmus Erlemann
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Barbalat’s Lemma to show the stability of equilibrium point x=0

I have this problem to solve: Use Barbalat’s Lemma to show the stability of equilibrium point $x=0$ for the system $\dot{x}=-x+p\sin(t)$ and $\dot{p}=-p\sin(t)$.
zahra
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Symbolic (analytic) solution to a nonlinear algebraic equation

I have obtained a set of three nonlinear algebraic equations resulting from conservation laws for momentum and kinetic energy. $$ \begin{align} m_1 V_1 \cos(\theta) + m_2 V_2 \cos(\alpha) & = m_1 V_0 \tag{1}\\ m_1 V_1 \sin(\theta) - m_2 V_2…
Fat32
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Can these equations be solved via substitution?

I have eight equations with variables $\{a,b,c,d,e,f,g,h\}:$ $$a*b*c*d=64\\ b+c+d-e=6\\ a*e=8\\ b+f=6\\ b*f=8\\ c*g=8\\ d+h=9\\ d*h=8$$ I know there are 4 solutions, but is there any deterministic way of solving these? I would like to figure out…
Carl Hill
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Solving Analytically 2nd order Nonlinear ODE

How to solve: $$\displaystyle \ddot{y} + 3 y \dot{y} + y^3 - t^{-1} (y^2 + \dot{y}) - 2 t^{-2} y - 4 t^{-3} =0$$ ? where $\dot{y} = \frac{dy}{dt}$ The solution $ y= j t^{-1}$
Mohamed Essam
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If two plotted meshes of nonlinear equations in a system intersect, does that mean there are always infinite solutions?

I am trying to wrap my head around this, as I have no formal education on it. I have a system of two nonlinear equations, with two variables. If I plot them in Matlab/Octave, and get two intersecting meshes, does that mean all the points where the…
Zach
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How to reduce system of non linear equations to a polynomial root finding problem?

I have a set of 5 non-linear equations: $w_0 + w_1 + w_2 = 1$, $w_0v_0 + w_1v_1 + w_2v_2 = a$, $w_0v_0^2 + w_1v_1^2 + w_2v_2^2 = a^2 + b^2$, $w_0v_0^3 + w_1v_1^3 + w_2v_2^3 = a^3 + 3ab^2$, $w_0v_0^4 + w_1v_1^4 + w_2v_2^4 = a^4 + 6a^2b^2 +…
AnthonyPadua
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System of two nonlinear equations in two variables

I would like to solve the following system of equations, where $x \in \mathbb{R}$ and $y\in \mathbb{R}$ are unknowns and $a,b,c,d,e \in \mathbb{R}$ are constants $(x+\frac{1}{x} -a)/(\frac{x}{y}+\frac{y}{x} -e)…
Fabio Dalla Libera
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