Computational Science Stack Exchange
Computational Science Stack Exchange

Questions tagged [nonlinear-equations]

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

A nonlinear system is a system which does not satisfy the superposition principle, i.e., meaning that the output of a nonlinear system is not directly proportional to the input.

350 questions
7
votes
3 answers

Convergence of fixed point iterations of a non-linear matrix system

I'm working on modeling two phase immiscible flow in a porous medium. When I setup the system of equations, I obtain a non-linear system of equations that can be expressed in the form: $A(x)x=b$ where the matrix $A(x)$ is a function of the…
Paul
  • 12,045
  • 7
  • 56
  • 129
4
votes
1 answer

Switch branch in bifurcation

I have a system of nonlinear equations $F(x,a) = 0$ and I know that at a specific point $a_c$ a bifurcation occurs, thus the Jacobian becomes singular. How can I switch branches and start following a new solution path as I increment $a$?
chemeng
  • 203
  • 1
  • 6
3
votes
1 answer

Period-doubling bifurcation, quasi-periodicity and dimension of torus

This is more of a conceptual question but closely related with how non-linear dynamics simulations results should be interpreted. I am confused about the relationship of "period" in the context of period-doubling bifurcation, quasi-periodicity and…
Axel Wang
  • 197
  • 7
3
votes
1 answer

Solving a non-linear heat equation with the galerkin method gives negative values

I am trying to solve a non-linear time-dependent heat equation $$\partial_tT=\nabla \left(k_T(T)\nabla T\right) + f$$ using the galerkin method, with neumann boundary conditions. For linearization of the nonlinear part I am using the newton…
arc_lupus
  • 543
  • 4
  • 17
2
votes
0 answers

Pros and cons of optimization vs. variational calculus, re: nonlinear elasticity

I'm trying to solve a problem of finding the displacements of an elastic material subjected to external forces. Those external forces are themselves a nonlinear function of the material displacements. The first step is to define a functional for…
OskarM
  • 297
  • 1
  • 10
2
votes
1 answer

Solving this system of equations numerically

In a personal project of mine, I've derived a couple of equations. $$ \sum_{j=1}^Nu_{ij}^*(\theta_1,...,\theta_N,J) - k_{i} = 0 \qquad \forall 1\leq i \leq N$$ $$\sum_{i
hoolaboris
  • 21
  • 1
2
votes
0 answers

Backing out a function of parameters from system of nonlinear equations

I have a system of equations that cannot be solved for in closed form: $F_1(x_1,x_2,\beta)=0 ~\&~ F_2(x_1,x_2,\beta)=0 $ I want to solve for functions $x_1=x_1(\beta) ~\&~ x_2=x_2(\beta)$ My approach so far: Fix $\beta=\beta_1$ Solve system…
VCG
  • 121
  • 2
1
vote
0 answers

Visualizing a low-dimensional torus in a high-dimensional system

In the 4D Henon-Heiles system, it is well-known for certain parameters the attractor is a 2D torus. I am wondering how can we plot this actual torus (embedded in 3D) by somehow projecting all 4 components to some 3D space and to observe if a…
Axel Wang
  • 197
  • 7
1
vote
1 answer

Initial condition for Kuramoto-Sivashinsky

For a project in my advanced numerical method class I have to solve the 1D Kuramoto-Sivashinsky equation of which I know little. I just know that it was derived the equation to model the diffusive instabilities in a laminar flame front. It reads…
user33890
1
vote
2 answers

finding wave function for anharmonic oscillator

I'd like to find the normalized ground state wavefunction for the anharmonic oscillator (Duffing) whose potential for which there is no analytic solution; an oscillator with a quartic potential, in addition to the quadratic potential. Any comments…
David H
  • 121
  • 4
0
votes
1 answer

How do I extrapolate data from a NON-LINEAR (logarithmic) standard curve in Excel?

I have made a standard curve. The X-axis is logarithmic. The y-axis is linear. I have added a logarithmic trendline (y = -1.546ln(x) + 39.254; R² = 0.9906). How can I re-arrange the equation to calculate an unknown X-axis value?
Jessica Oliver-Bell
  • 1
  • 1
  • 1
  • 1
0
votes
1 answer

Solving $\sum_i^d a_i \exp(-q_i k)=b_0$ for $k$

Suppose $a_i,q_i,b_0$ are positive real numbers. I need to solve the following equation for $k$ $$\sum_i^d a_i \exp(-q_i k)=b_0$$ Is this a well-known problem? One my special cases has $a_i=q_i$ In my application $d> 20000$, $q_i\approx 0$.…
Yaroslav Bulatov
  • 2,655
  • 11
  • 23
0
votes
0 answers

Best way to solve system of quadratic forms

I have a system of equations that have the following structure. Let $x\in\mathbb{R}^m$ and let $x_k$ be the $k$-th element of $x$. Let $H_k\in\mathbb{R}^{m\times m}$ for $k=1,\ldots, m$. I need to find the $x$ satisfying, \begin{align} x_k = x^\top…
5d41402abc4
  • 183
  • 2
0
votes
3 answers

Initial conditions for pendulum Jerk equation

I have a very simple problem, but can't seem to understand what I need to do. In simulating a pendulum from it's jerk equation, I'm having a hard time setting initial conditions to get it to work out. So for example the equation of motion for a…
Josh
  • 217
  • 2
  • 6
-1
votes
1 answer

solving a non-linear equation with integrals involved

I would like to solve the following equation, wrt $n(e)$ $$f(n(e))=g(n(e)) + \int_{\alpha}^{e} w(n(x))dx $$ The integral there it confuses me. Any suggestion on how I can implement this on a the computer (I am mostly Matlab user) thanks UPDATE or…
user17880
  • 235
  • 1
  • 6