# Questions tagged [newton-method]

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

133 questions
Filter by
Sorted by
Tagged with
102 views

1 vote
137 views

253 views

### 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 ...
259 views

### Backward Euler + Quasi Newton(Broyden) method fails to solve Van der Pol's equation(Stiff ODE)

The first guess is using the forward Euler approach. The first jacobian is using finite differences. Then NR method is used to solve for the next iteration and Broyden's method is used to update the ...
137 views

### Applying displacement control loading using lagrange multipliers in the material non-linear finite element method

Hi I am trying to implement a simple plasticity based finite element code. I am not clear how to set up displacement control applied through Lagrange multipliers. In case of a linear problem, I did ...
1 vote
60 views

83 views

### Newton-Raphson for estimating Weibull distribution does not converge

I've been trying to estimate the two-parameter (a,b) Weibull distribution (loc. param. = 0). $$f(t;a,b)=\frac{b}{a}\left(\frac{t}{a}\right)^{b-1}\exp(- \left(\frac{t}{a}\right)^b)$$ To find the ...
1 vote
635 views

### Drawing saddle node bifurcation diagram for a non-linear ODE in Python

I'm trying to draw the bifurcation diagram of the following ODE, This ODE leads to a saddle-node bifurcation (see wiki) However what I get is not exactly right. There's a lot of "noise" as ...
232 views

### Numerical Methods of solving a non-linear ODE?

I want to solve the nonlinear equation $\frac{d^2x}{dt^2} + k\sin x = 0$, numerically. I found that solving this elliptic integral would be cumbersome, so is there a numerical method i could use to ...
1 vote
72 views

### Solution predictors for accelerating convergence in nonlinear FEM

I am looking for the details of commonly-used predictors for accelerating the convergence of iterations using Newton-Raphson scheme for nonlinear problems in FEM. I am looking specifically for static ...
196 views

### Coding up Newton's method for a mapping from R^2 to R -- the Jacobian wouldn't be invertible

I'm trying to code up in Matlab a multivariable Newton's method, for a mapping from R^2 to R, but the Jacobian would be a 2x1 matrix, not square, so it wouldn't be invertible. Does this mean that ...
213 views

### Solving system of nonlinear vector functions

I am trying to figure out how to implement a solver for a system of nonlinear equations of the form \begin{align*} u_1 &= y_n + h\left(a_{1,1}f(t_n + c_1 h, u_1) + a_{1,2}f(t_n + c_2 h, u_2)\...
1 vote
53 views

### Quadratic optimization with nonlinear vector term

I wish to minimize the quantity $$W=1/2x^TAx-x^Tg(y)$$ with respect to $x$ and $y$, which are vectors of unknowns. $A$ is a sparse square symmetric positive definite matrix and $g(y)$ is a vector with ...
62 views

### Convergence of Truncated Newton for non-convex Hessian

I was wondering if anyone could enlighten me about the convergence properties of the truncated newton method in case of a non-positive definite hessian $\nabla^2 f = H$. From the Book 'Numerical ...
36 views

913 views

### 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 ...
1 vote
910 views

### 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 ...
510 views

### 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 ...
1 vote
113 views

458 views

### 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 ...
685 views

### How to calculate/derive analytic FEM Newton Jacobian

I trying to wrap my head of derivation of the analytic FEM Jacobian for the Newton method. Say we have a nonlinear Poisson problem of the (weak) form $$\int a(u)\nabla\ u\cdot \nabla v = \int f v$$ ...
1 vote
366 views

### 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) ...
951 views

### GMRES vs Newton-GMRES for Solving nonlinear PDE's

Often when numerically solving nonlinear PDE's using method of lines approach with an implicit integrator a system of nonlinear equations have to be solved. To be more specific, let's say we have ...
142 views

229 views

### Imbalance of variables in Mixing Newton's method and Linear solver for a Non-linear system

Problem Solving a non-linear system of equations. The number of variables is the same as the number of equations. When I fix a set of variables (say $\vec{y}$) and keep another set free (say \$\vec{...