Questions tagged [nonlinear]
Used to mark questions about nonlinear differential equations, `NonlinearModelFit`, and related to nonlinear dynamics.
717
questions
2
votes
2
answers
208
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Solve can’t solve this… is there a way to approximate it?
I've been toying around with mortgage/loan calculations and spreadsheeting. The loan formula is as follows:
A = p * r *(1+r)^n / ((1+r)^n - 1)
A: payment per period
p: principal
r: interest rate
n: ...
3
votes
2
answers
327
views
How to solve transcendental coupled equations?
Dear Mathematica users,
I am trying to solve the following system of transcendental equations,
$$
f(\eta,y,\theta) = y - \frac{2}{\eta}{\textrm{Coth}(\frac{3 y \eta}{4 \theta})}=0,
$$
$$
g(\eta,y,\...
- 447
0
votes
0
answers
51
views
Solving coupled system with nonlinear 3rd order ODEs, over range from zero to infinity
I need help solving this system with the fifth-order Runge Kutta Fehlberg integration scheme.
my code is
`
...
0
votes
0
answers
89
views
Mathematica doesn't solve Friedmann's equation, how to proceed?
I'm working on a especific cosmological setting that culminates in the following equation: (https://i.stack.imgur.com/YESWs.jpg). But when I try to solve it through the DSolve method in Mathematica I ...
0
votes
1
answer
94
views
Non linear second order ordinary differential equation in general relativity
I am working on general relativity, and the so called Bonnor's model, published in 1989 (General Relativity and Gravitation Vol 21 # 11 , 1989 Negative mass in general relativity ).
From the ...
- 73
1
vote
1
answer
70
views
Solve Equation with NSolve
I am trying to solve nonlinear equation in mathematica, the equation include the function Erfc which is defined in mathematica, the equation is true and I should for sure get answer. but for some ...
- 147
6
votes
2
answers
426
views
How to force fit of the data to exactly match one of its points?
Consider the following data:
...
- 5,102
1
vote
1
answer
60
views
Obtaining different answers when using NDSolve vs ParametricNDSolveValue
I am obtaining two different answers for a curve when solving the same exact system of differential equations when using NDSolve vs when using ParametricNDSolveValue. Here it is when using NDSolve:
<...
- 69
3
votes
1
answer
80
views
Nonlinear model Fit [closed]
I am trying to fit my data to the function:
a + (b*(c/2)^2)/((T - d)^2 + (c/2)^2)
I entered
nlm = NonlinearModelFit[data,
a + (b*(c/2)^2)/((T - d)^2 + (c/2)^2), {a, b, c, d}, T]
However it returned
[0....
- 33
1
vote
1
answer
71
views
Convergence problems Non-Linear FEM
I am trying to solve a 1D non-linear ODE with FEM. The ODE corresponds to a Model with 3 parameters ([Beta], [lambda], A_2). The ODE reads
mpl/(m^2)Cos(z)^4 f''(z)-2mpl/(m^2)Cos(z)^4Tan(z)f'(z)-A2\rho(...
- 147
0
votes
0
answers
46
views
Finite Difference and LinearSolve
I have two nonlinear second order coupled boundary value ODE whose dependent variables are $u(x)$ and $z(x)$. I want to solve it using the Relaxation method (Finite-Difference), however, I can't ...
- 499
9
votes
2
answers
239
views
Curve tracing for a given data set
I want to trace the curve for the given data set.
This is my code
...
- 1,094
2
votes
2
answers
101
views
How can I find an intermediate function between a set of functions?
I have 5 nonlinear functions, which are very complex and long. For this reason I will not include them here. But the plots of four of them are given here:
I am looking for some functionality which ...
- 989
3
votes
1
answer
111
views
LinearSolve used in Iteration is extremely slow
I'm trying to solve the nonlinear second order boundary ODE where the method I'm using is Relaxation method for ODEs,
$$z''(x)-\frac{\frac{1}{100} z(x)^4 \left(2 z'(x)^2+12\right)-600 \left(z'(x)^2+1\...
- 499
0
votes
0
answers
40
views
Encountered a singular Jacobian while solving nonlinear equations
I am solving the nonlinear questions in equation 4.1a-4.1c given in the paper. (https://arxiv.org/pdf/cond-mat/0008249.pdf) but no success.I posted similar questions in the link Encountered a singular ...
- 51
3
votes
1
answer
87
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Encountered a singular Jacobian while solving nonlinear equations
I am solving the nonlinear questions in equation 4.1a-4.1c given in the paper.
(https://arxiv.org/pdf/cond-mat/0008249.pdf) but no success.
...
- 51
2
votes
1
answer
35
views
Replace Subscripts in FindRoot solution to a boundary-value problem
FindRoot has a nice example to solve a boundary-value problem for a second-order ordinary differential equation using "collocation points" to turn the ODE ...
- 213
2
votes
1
answer
196
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Nonlinear Boundary ODE and FindMinimum
I have a functional $S$,
$$S = \left( \int_{x_0}^{x_f} dx \frac{1}{z^d} \sqrt{-f(z,u) u'^2 - 2 u' z' +1} \right) + \frac{1}{z(x_0)^{d-1}}$$
where it is composed of two terms, i.e. an integral plus a ...
- 499
3
votes
2
answers
169
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Non-linear integro-differential equation with infinite domain of integration
$$I(t)=\frac{dy(t)}{dt}+\int_{-\infty}^t dt'\left[\sin\left(\frac{y(t)-y(t')}{2}\right)f(t-t')-\sin\left(\frac{y(t)+y(t')}{2}\right)g(t-t')\right]$$
with $y(t\leq 0)=0$ and $I(t)=I_0\Theta(t)$ with $\...
0
votes
1
answer
61
views
Check if NDsolve solution of nonlinear second order eq. is random
I'm solving second order nonlinear eq. using NDsolve. I'm interested in y'(t) dynamics (plotted below). The thing is - from this solution I'm not sure if we have some randomness or it is just complex ...
- 171
5
votes
1
answer
223
views
Solving Coupled nonlinear Differential Equations For Eigenvalue And Eigen functions
I tried to solve coupled nonlinear differential equations from this paper https://sci-hub.hkvisa.net/10.1016/j.jcp.2019.109058 to see eigenvalues and eigenfunctions in different dimensions. At first, ...
- 279
3
votes
1
answer
106
views
1
vote
1
answer
163
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NDSolve unable to solve nonlinear differential equation
I have an action $S$,
$$S = \int dx \frac{1}{z^d} \sqrt{1 + \frac{z'(x)^2}{f(z)}}$$
where the Lagrangian $L$ is,
$$L = \frac{1}{z^d} \sqrt{1 + \frac{z'(x)^2}{f(z)}}$$
I want to plot $z(x)$ and solve ...
- 499
11
votes
1
answer
424
views
Solving Stochastic Gross-Pitaevskii equation
I am trying to solve the Stochastic Gross-Pitaevskii equation from this paper https://arxiv.org/pdf/1409.0146.pdf. But I have no idea how to solve adding a noise term.
I like to see the wave function ...
- 279
1
vote
1
answer
187
views
Highly coupled nonlinear second order differential equations
I have an action given by,
$$S = \int dx \frac{1}{z^d} \sqrt{-f(z,u) u'^2 - 2 u' z' +1}$$
The dependent variables are $u$ and $z$ for which they are dependent on the parameter $x$. The equation of ...
- 499
0
votes
0
answers
60
views
DSolve giving error output solving a nonlinear PDE
I try to solve the following PDE:
sol = DSolveValue[D[u[x, t], {t, 1}] == D[u[x, t], {x, 2}]/D[u[x, t], {x, 1}], u[x, t], {x, t}]
the output is:
...
- 1
2
votes
2
answers
90
views
Insufficient memory in Nonlinear Model Fit with ParametricNDSolve
I try to fit parameters to ODE solver with chemical kinetic eqations:
...
- 225
3
votes
1
answer
217
views
Solving 3D Nonlinear Integral Partial Differential Equation
I am trying to solve Equation number (1.2) numerically in MATHEMATICA. This equation is solved in the papers https://arxiv.org/pdf/2205.05193.pdf, https://arxiv.org/pdf/2202.13264.pdf, and https://...
- 279
2
votes
1
answer
81
views
How to properly fit experimental data to a nonlinear model?
So I'm trying to fit experimental data to a nonlinear model using the NonLinearModelFit command, but it isn't quite working.
The plotted data set looks like this:
The data is to be fitted with
...
1
vote
1
answer
115
views
Plotting the solution of nonlinear 2-dimentional system of ODEs
I am new to Mathematica, and I have a 2-D system of ODEs:
dx/dt=y
dy/dt= -x+x^3-2my
Mathematica code:
...
- 93
2
votes
1
answer
99
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Nonlinear complex ODE system modeling modified harmonic oscillator coupled to quantum harmonic oscillator
I'm using NDSolve for a system of non-linear ODEs. Here is my code
...
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6
votes
3
answers
533
views
How do I solve this matrix equation for infinitesimal rotations?
I have a matrix equation, taken from Wikipedia (Infinitesimale Drehungen), that looks not that complicated (note $a$ is a scalar, actually an angle as input paramter for the rotation matrix):
$$
R(a)=\...
- 315
1
vote
1
answer
104
views
Newton method and Armijo-Goldstein
I need help with my project. I have three nonlinear systems and I need to write a code for Newton methods and Armijo-Goldstein and see the differences.
...
- 11
9
votes
3
answers
1k
views
NonlinearModelFit's fit is atrocious
I want to do a very complicated fit (it involves a product of polynomials and non-linear functions).
I read about NonlinearModelFit and thought it would be a good idea to use it. I started with a toy ...
- 1,212
2
votes
1
answer
158
views
Solving 2D Coupled Nonlinear SO Coupled Equation
I am trying to solve coupled nonlinear SO coupled equations in 2D from the following two papers https://arxiv.org/pdf/2105.08849.pdf and https://arxiv.org/pdf/2109.00491.pdf. They have given an input ...
- 279
2
votes
1
answer
110
views
Lyapunov exponents at a fixed point
I am trying to find the Lyapunov exponents at a fixed point as given in the paper here(page 14). The code that I have used till now is given below:
...
- 669
2
votes
1
answer
114
views
Solving logarithmic 2D Nonlinear GPE Equation
I am trying to solve the logarithmic 2D Nonlinear GPE Equation from this paper https://arxiv.org/pdf/1801.10274.pdf. But failed to get the ground state solution and vortices. I tried to solve in ...
- 279
3
votes
1
answer
104
views
How to solve PDEs for function $\Psi(z,\bar{z})$ dependent on independent variables $z,\bar{z}$? (Wirtinger derivatives)
For the past few days, I have been struggling to convey to mathematica to solve a PDE that is in terms of the independent variables $(z,\bar{z})$. I know mathematica supports solving PDEs with respect ...
- 133
2
votes
1
answer
118
views
How to fit experimental data using NonLinearModelFit
I am trying to fit the experimental data with the below equation but I am failing to get a good fit
This is the data
...
- 77
4
votes
4
answers
283
views
Simultaneous nonlinear fitting of two datasets to two trial functions with shared parameters
I'm relatively new to mathematica and stack exchange.
Problem
Generally my problem concerns finding a simultaneous fit of multiple functions to multiple datasets with shared parameters. I have looked ...
- 107
10
votes
1
answer
440
views
Are there practical Mathematica tools for detection of limit cycles in two dimensional dynamical systems?
I have a dynamical system with one boundary saddle point, and one unstable interior point, and I would like to detect existence of cycles. This is of course a hard problem if the cycle is very small, ...
- 1,314
2
votes
2
answers
155
views
Fitting on Diffraction Pattern, NonlinearModelFit, Complex Infinity
I'm trying to fit the function
$f(x;a,b,s)=a\left( \frac{\sin\left(b \sin(s x) \right)}{b \sin(s x)} \right)^2 $
on the data below using NonlinearModelFit but I'm ...
- 153
0
votes
0
answers
51
views
Is it possible to make Mathematica find a solution to this first order system of nonlinear ODE?
The first order system of 4 coupled ODE with trigonometric terms is the following:
$$
\begin{array}{rcl}
\dot x(t)&=&y(t)\\
\dot y(t)&=& -A \sin(x(t))+\frac{v(t)}{B}\\
\dot u(t)&...
- 933
0
votes
2
answers
126
views
NONLINEAR EQUATIONS cannot get the solution
I have simplified the equations and decrease the variables to 5, and changed the parameters' value as I think the equations in enter link description here is because of the improper parameters' value.
...
- 65
1
vote
2
answers
156
views
FindRoot::jsing: Encountered a singular Jacobian at the point when solving NONLINEAR EQUATIONS
I have tried many methods to solve the following nonlinear equations.
...
- 65
1
vote
0
answers
77
views
Three nonlinearly coupled PDEs
I am new to Mathematica and I need it to solve a system of three nonlinearly coupled PDEs.
$\frac{n_1}{c_0} \frac{\partial E_1}{\partial t}+\frac{\partial E_1}{\partial x} = i\frac{\omega_1}{2n_1 c_0} ...
- 11
0
votes
0
answers
61
views
Solving numerically Non linear Differential Equation
I am trying to solve the following D.E. with the dependent variable "H" and independent variable "r" and "t":
...
- 1
2
votes
0
answers
38
views
Function only returns first interpolating function after parameter values specified?
I am fitting data using a system of coupled differential equations and have defined a model function like so:
...
- 399
2
votes
1
answer
247
views
Goodness of fit [closed]
I want to evaluate the goodness of two sets or more fitting parameters, using Rsquared and RMSE (root mean square error), Then how to code?)
...
- 33
1
vote
1
answer
119
views
Finding fit parameters for a 2-dimensional matrix of data if the value of some parameters depend on the row and others on the column
I have some 2-dimensional data of dimension n x m that I suspect has the following structure:
...
- 121