# Questions tagged [nonlinear-equations]

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

304 questions
Filter by
Sorted by
Tagged with
79 views

### Is it possible to use a fixed point iteration for solving this nonlinear system?

Consider the following differential equation \begin{align} \frac{\partial f(u)}{\partial x} &= g(x), \ \ x\in [x_{L},x_{R}] \label{Eq2.2} \\ u(x_{L}) &= g_{1} \end{align} where $f(u)$ is a ...
114 views

### Analysis of nonlinear finite element methods

I have been doing a lot of reading on the development of finite element methods and their analysis using, e.g., functional analysis. I am clear on the formulation of the weak form of a PDE and ...
45 views

139 views

### How to discretize a non-linear PDE with boundary conditions and intial value

Consider this non linear PDE: $$u_t + c(u^2)_x =\alpha u_{xx} \text{ , } -1<x<1 , t>0$$ with $$u(-1,t) = g_L(t) \text{ , } u(1,t) = g_R(t) \text{ and } u(x,0)=f(x)$$ where the 3 functions(...
93 views

### How does the error work for the Strang Splitting?

We know in Strang splitting that the splitting error in the steady state solution is proportional to $h^2$. I want ask 2 things: If this error in the steady state solution is the global error? If we ...
113 views

### Discretization of a non-linear ODE using FDM isn't grid indepenent

I am trying to solve the ODE : $\frac{d^2T}{dx^2} = \omega_1 T+\omega_2 T^2$ + using different numerical methods. I have tried the following discretizations so far and none of them seem to be grid ...
31 views

116 views

71 views

55 views

74 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 ...
637 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. ...
128 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 ...
76 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 $\beta$ ...
75 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 ...
88 views

### Methods for solving discrete PDEs using algorithmic differentiation results

I'm looking for a method to solve a 20000 variable, 20000 residual non-linear PDE with a Galerkin method. I have Fortran subroutines for: The residuals: $\vec{r}(\vec{x})$; Their Jacobian multiplied ...