# Questions tagged [newton-method]

Method for finding successively better approximations to the roots (or zeroes) of a real-valued function

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### Solving long time averaged chaotic nonlinear equations

I have a modified chaotic equation of the form: $$\frac{\partial u}{\partial t} = - (u+c)\frac{\partial u}{\partial x} - \frac{\partial^2u}{\partial x^2} - \frac{\partial^4u}{\partial x^4}$$ I am ...
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### Jacobian-free approach for time-dependent equations for implicit time-stepping

When solving time-dependent non-linear equations, such as the non-linear diffusion equation $$\partial_tu=\nabla\left(D(u)\nabla u\right)$$ usually Newton's method is applied, with (coupled with the ...
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### Parallelizing Newton-method in solving non-linear systems

Circuit simulation software based on SPICE (such as ngspice) uses Newton-Raphson method to solve non-linear system of equations ...
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### How to avoid gsl root finder evaluate function outside its domain

When I use the newton's method or hybrid solver in the GSL package to deal with 1-D or multidimensional root solving problems, the code frequently crashes when the solver requests function value ...
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### Evaluation of slope at iteration ith - Newton-Raphson method

I'd like to know how Ansys computes the slope (=stiffness matrix) at point x1 in figure. I'm studying the way in which Ansys uses the Newton-Raphson method when there are nonlinearities. In the slide ...
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### Number of GMRES iterations increase when stepping forward in time, using the Newton method

I am solving a system of nonlinear time-dependent equations using the Newton method in a finite-element-setting, i.e. first I create the jacobian matrix for the current time, and afterwards I try to ...
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### How to use Newton-Raphson method to handle nonlinear terms in coupled system of PDEs?

I'm trying to solve the Nonlinear Schrodinger's Equation (NLSE) in 2D using Finite Elements, but I don't know how to handle the nonlinear term. I suppose I have to apply the Newton-Raphson algortihm ...
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### How to use Wolfe-Powell step-size control in quasi-Newton method?

I'm trying to find the minimum of a function using the quasi-Newton method with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. But I want to change the following implementation, so that: 1) ...
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