# Questions tagged [nonlinear-analysis]

For questions on nonlinear analysis, a branch of mathematical analysis that deals with nonlinear mappings.

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### Brent's Method convergence criteria

I am using Brent's method to solve the BEM equations for a wind turbine model. I have run into a scenario where Brent's method has converged i.e., abs(m) is below set tolerance of 1e-8 but the value ...
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### Backstepping control of second order nonlinear system

$\dot{x_{1}}=x_{2}^2-3\sin(x_{1})x_{2}$ $\dot{x_{2}}=x_{1}^3-3x_{2}\cos(x_{1})+u^{1/2}$ Question: Using the backstepping method and Lyapunov function, design the controller $u$ that will make the ...
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### Mathematics of apportionment of representation in a legislative body

It seems to be eclipsed by coronavirus, but today is the U.S. Census day for this coming decade. If you are American, where you are living today, where your children are living today, is where they ...
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### Non-Linear Differential Equation with quadractic terms

I have been doing some exercises about solving differential equations, but I am not be able to solve this one: Find the implicit solutions of the following DE $$\dfrac{xx'}{\sqrt{x^2+r(x')^2}}=c,$$ ...
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The problem is probably just for fun or maybe somehow related to so-called nonlocal ODE/PDE theory. Two facts: the solution to $u_x(x)=u(x)+u(-x)$ is only the zero solution. the solution to $u_x(x)=... 0answers 29 views ### Non-linear maps between Fréchet spaces - is this property well know? Let$E$and$F$be Fréchet spaces and$f:E\rightarrow F$a (not necessarily linear) map. We call$f$bounded, if it maps bounded sets of$E$into bounded sets of$F$. If$f$is linear, then ... 0answers 23 views ### Possible phase difference in equation of sine functions Given the equation$ A_1\sin(\omega t + \theta_1) + A_2\sin(\omega t + \theta_2) + A_3\sin(\omega t + \theta_3) = 0 $which holds for all$t$. It seem apparent that this implies that the phase ... 1answer 43 views ### Is$T$a nonlinear map? [closed] Define$T:\Bbb R^2\to \Bbb R^2$with$(x,y)\in\Bbb R^2$and$(e^x,e^y)\in \Bbb R^2$s.t.$\forall x,y(x,y)\mapsto (e^x,e^y).$Define the origin to be$(0,0)$before the map and after the map. This ... 0answers 21 views ### Third order linear differential equation and Painlevé II solution Consider the solution to the Painlevé II equation on$\mathbb{R}$$$q''=2q^3+rq$$ with the boundary condition$q(r)\sim_{r\to +\infty} \mathrm{Ai}(r)$and consider the function$f$such that for$r\...
Consider the following example: I have a big set of test data with input $x$ (of dimension 10) and output $y$. The plot $y$ vs $x$ shows that $y$ depends nonlinear on $x$. I want to construct a ...