# Questions tagged [nonlinear-equations]

Solution of nonlinear systems of equations. The equations might be algebraic or differential equations.

293 questions
Filter by
Sorted by
Tagged with
51 views

### Continuous limit and nonlinear functional analysis

I have a kind of general question about approximation schemes in nonlinear functional analysis. Given a nonlinear map $\Phi$ from an open set (in an infinite dimensional Banach space) of functions to ...
46 views

### Solving two coupled non-linear second order differential equations numerically using python [closed]

Please help with the following Python code for a nonlinear coupled oscillator, I am getting an error, I don't understand the problem. ...
13 views

71 views

### Interpreting multivariable root-finding results from Matlab's fsolve algorithm

Edit: So I was able to get the same value of r that's given, when coding up the sum of squares of function values directly in the script file, rather than on the Command Window. So, maybe there's a ...
26 views

69 views

### Derivative-free ill-conditioned non-linear least squares

I am looking for a package which can solve (non-linear) least squares problems without the use of derivatives (because of an expensive model), but which also deals with ill-conditioning well (such as ...
335 views

### Jacobians with automatic differentiation

I have an objective function F: Nx1 -> Nx1, where N>30000. There are many sparse matrix/tensor multiplications in this function, so taking an analytic Jacobian by paper and pen is cumbersome. ...
94 views

### How avoid square shape with Laplacian operator in reaction diffusion calculations?

I have used different variants of the Laplacian operator (div grad) using 4, 8, 12, 20 and 24 of the closest points. I get problems due to the chosen coordinate system and the discretization of the ...
58 views

### Integrating a nonlinear ordinary differential equation

I am solving an equation of the form $(*)$ $0 = a(f) (\partial_rf)^2 + b(f) (\partial_rf) + c(f),$ where $f$ is a real function of $r\in \mathbb{R}$, and $a,b,c$ are real functions of $f$. The ...
73 views

### RK4-method starts oscillating above certain input parameters

I am trying to solve an equation of the following type $$\partial_zE(z)=-c_0J$$ with $$J=c_1\beta E^3(z)$$ using the boost::odeint-framework and a fixed time stepper, with $c_0$, $c_1$ and $\beta$ ...
73 views

### Issue solving nonlinear equation containing a quotient

I have a coupled set of PDEs that need to be solved as part of a larger problem. I am currently approaching this by computing spatial derivatives with finite differences and using PETSc's nonlinear ...
100 views

2k views

### Solving a linear equation system with pure Neumann condition

I am trying to solve a linear equation system $\textbf{A}\textbf{x}=\textbf{b}$, e.g. a Poisson equation discretized in strong form, using biCGstab method. Since there are only natural Neumann ...
764 views