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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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Where do we find theory and applications of Products of Sums?

M. D. Newcomb used a Product of Sum operator in resolving conflict within binary petri nets. What math theory does this apply to? What other applications has this been applied to?
D.W. Boren
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state space linearization

I am trying to linearize the non-linear state space model of: $\dot{x_1} = \frac{1}{C_p}(i_{pv} - x_2u)$ $\dot{x_2} = \frac{1}{L}(R_o(i_o - x_2) - R_Lx_2 - x_3 + (V_D + x_1 - R_mx_2)u) - \frac{V_D}{L}$ $\dot{x_3} = \frac{1}{C_o}(x_2 - i_o)$ So I…
user2913869
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Newton method for nonlinear system

Use Newton’s method (and indicate each successive approximation) to solve the nonlinear system below for $x_1$ and $x_2$ both near $0.6$: $$x=\sinh⁡(y)\\ 2y=\cosh⁡(x)$$ I found the Jacobi matrix, found it's inverse and used the formula: Xo-inverse…
user3281911
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Solution to a nonlinear set of equations

There is a set of $n$ nonlinear equations of the form $f_i(x_1,\dots,x_n)=\gamma_i$ where $x_1,\dots,x_n $ are real non-negative variables, $i\in\{1,\dots,n\},$ and $\gamma_i\in \mathbb R$. The function $f_i$ is increasing in each variable…
triomphe
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grade 10 linear systems question

i am stuck on this question and don't know how to show my work. the question is, John invests $1000 in mutual funds and bonds. If bonds earn 6% and mutual funds earn 8%, how much should he invest in each so that the interest from the mutual funds is…
jim
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Convergence in Newtons Method when derivative is replaced by some constant.

Suppose we replace the derivative by $d$ in Newtons method, i.e. $$ x_{k+1} = x_k - \frac{f(x_k)}{d}.$$ For what conditions on $d$ will this be locally convergent?
onimoni
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One iteration of newton's method on a system of nonlinear equations.

So we have the following set of nonlinear equations $$ x_1^2 - x_2^2 = 0, $$ $$ 2x_1x_2 = 1, $$ with starting value $x_0 = [ \: 0 ,\: 1 \: ]^T$. So, how do I do one iteration of newton's method? I know that for a nonlinear system of equations,…
onimoni
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How to solve this integral equation involving CDF of a random variable?

Suppose $F_X(x)$ is CDF of random variable $X$. I am going to find the value of $x$ such that the following equation is satisfied: $$ ax+bxF_X(x)+ c \int_{x}^{\infty} \left[ 1-F_X(y) \right] \text{d}y = 0 $$ where $a,b,c$ are known parameters. Is…
Amin
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Number of non-linear steps in range, without iterative calculation?

I want to quickly calculate how many steps S there are between some min and max, where n=min to start with, given some particular non-linear formula, e.g. n'=n * 1.01, n'' = n' * 1.01 etc. until n exceeds max. The simplest way to determine S is to…
Engineer
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Is this system of nonlinear equations well known?

Let let $i,l=1,...,N$, let $a_{i}$ and $b_{i,l}$ be some positive constants with $\sum_i b_{i,l} = \sum_l b_{i,l} = 1$ for all $i,l$. Let $f: \mathbb{R}^2 \rightarrow \mathbb{R}$. Consider the following system of equations in unknowns $x_{i},y_{i}$:…
Andres
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Critical Points of non linear differential equation

In this system of non-linear differential equation: $$ x' = (x-y)(x+y) \\ y' = (2+x)(5+y) $$ I'm getting four critical points $(-2,-2)$, $(-5,-5)$, $(-2,2)$ and $(5,-5)$ instead of three as suggested by the question textbook. Can anyone check?
Bhuvesh Mahajan
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Solving $3$ equations with $3$ unknowns when one of the equations is not linear

I have $3$ equation with $3$ unknowns $(i, j, k)$ while $a, b, c, d, e$ and $f$ are known. $$ai + bj + ck = 1\\ di + ej + fk = 1\\ i^2 + j^2 + k^2 = 1$$ This type of equation set is typical for unit vector solving problems. So I need to find the…
Vefa o
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Roots of a linear equation

UPDATE - I update this question today(28.12.2022), sorry for being not specific earlier. I have a bunch of solar panels, each one is connected to an inverter. For each solar panel I have two sensors, a wind and a west sensor. From every inverter, I…
rish
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Is equation system solvable?

Let's say we have $n$ binary unknowns (i.e. either 0 or 1), $x_1$ to $x_n$. And we have some equations similar to the following: $x_1 + x_2 + \dots + x_n = a_1$, $x_1.x_2 + x_3.x_4 + \dots + x_{n-1}.x_n = a_2$, $\dots$ $(1-x_1).x_2.x_3.(1-x_4) +…
xycf7
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solve non linear system with two variables

I want to solve a non linear system of two equations $x$ and $z$. I have two equations : $$ x^2-z^2-2 x z +1 =0,$$ $$ z^2-x^2 -2 x z +1 =0.$$ I know that there are two solutions $(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$ and…
ZchGarinch
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