Questions tagged [differential-equations]
Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
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0answers
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How to increase the integration domain of NDEigensystem without a “non-Hermitian” error?
Recently, I've been using NDEigensystem to solve a two-dimensional eigenfunction equation. The region that I'm solving over is as follows.
...
0
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0answers
50 views
Take limit in NDSolve
I have this equation :
eqkk =
D[k[t], {t,2}] - ((3 sola'[t]/sola[t]) + (3 sola''[t]/sola'[t]) -
(1/(sola'[t] sola[t]^2))) D[k[t], t]
To get $k(t)$:
<...
2
votes
1answer
66 views
Poincaré sections for oscillating system
I need to build Poincare maps for solutions of a system of differential equations. This system includes the mass of an oscillating particle. If the mass value is made very small (m ~ 10 ^ -25) the ...
0
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0answers
23 views
Could not able to set up a differential equations using EulerEquations command
I have a constructed the Lagrangian of a mechanical system by finding the kinetic and potential energy of the system. Then I tried using EulerEquations to set up a differential equation by taking the ...
0
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1answer
54 views
Using multiple boundary conditions with NDEigensystem
I'm quite new to Mathematica and to Stack Exchange so I apologise if this question has already been answered.
I've recently been trying to solve a partial differential equation to find the ...
0
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0answers
31 views
DSolve not giving a solution
I tried solving this but no result, I tried eliminating the initial condition, replace the zeroes in boundary condition but nothing is working.
Thank you in advance
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0answers
49 views
NDSolve problem with modified heat equation
I am having a problem while solving a modified version of the heat equation. The code is as follows:
...
0
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1answer
31 views
How to keep the numerical integration when a event occurs?
I'm numerically integrating the following system,
f[r_] = 0.904965 - (1 + 12.7028/r^2) (1 - 2/r)
dϕdλ = 1/r[λ]^2;
eqc = r'[λ] == Sqrt[f[r[λ]]/(dϕdλ^2)];
with the ...
1
vote
1answer
49 views
Stiffness and NDSolve error NDSolve::ndsz:
I have a 2nd Order ODE problem I am trying to solve numerically in Wolfram:
$$
(k^2-1+\frac{2x}{x^2+c^2})\frac{d^2y}{dx^2}+\frac{c^2-x^2}{c^2+x^2}\frac{dy}{dx}+x\frac{x^2-3c^2}{(x^2+c^2)^3}y=0
$$
...
0
votes
1answer
48 views
Solve Heat Equation with Source Term and Neumann BC
I am trying to find a solution on mathematica to
$ \partial_tu-\partial_{xx}u= \cos(2\pi x), \; 0<x<1,\; t>0 $
$ \partial_xu(0,t)=\partial_xu(1,t)=0, \; t>0 $
$ u(x,0) = \...
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0answers
38 views
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1answer
50 views
DSolve behaves weirdly with dynamic [duplicate]
I am an beginner in using dynamics as well as mathematica. I am trying to ask mathematica to solve and plot the solution of X'=AX with dynamic every time my matrix A updates. However the Dsolve ...
3
votes
2answers
105 views
How do I solve a certain differential equation?
I need to find out a solution to the equation:
z r[z] r''[z] - (d - 1) r[z] (r'[z])^3 - (d-2) z (r'[z])^2 -
(d - 1) r[z] r'[z] - (d - 2) z == 0
subject to the ...
0
votes
0answers
51 views
Problem with NDSolve and Manipulate function
I'm having an issue with commands NDSolve and Manipulate.
I'm trying to represent the rotation spin, nutation and precession of a spinning top (approximated to an inverted cone).
Under specific data ...
1
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2answers
79 views
Fitting experimental data with a parametric function
How does one use a fitting routine such as NonlinearModelFit with a ParametricFunction? Example below:
First let's generate some data:
...
2
votes
1answer
65 views
ParametricFunction from ParametricNDSolveValue changes when evaluated?
I am new to using ParametricNDSolveValue (and ParametricFunctions in general), so I am hoping that I have made a simple error. First I set up a system of differential equations:
...
1
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1answer
44 views
How to provide a system of input every x time interval (e.g, x=1 week)
The following code described an input to the system only during t less than minInfusionTime after time zero. Any way to give this same input every x time (e.g. every week) after time of zero, to an ...
0
votes
1answer
54 views
DSolve not working on vector equation
Ok, so I'm trying to solve a differential equation of motion, and mathematica doesn't do anything to my input. It just leaves it unevaluated. I know that the system is physically solvable with not ...
4
votes
2answers
99 views
Non Linear Model Fit - Fitting ODE to Data
Thank you everyone for your meaningful contributions!
My Goal and Problem
I'm trying to fit a particular ODE in a set of ODE's to experimental data. I've attempted to implement this by following the ...
0
votes
2answers
52 views
Parametric Find Maximum
I'd like to plot the maximum of a curve in function of a parameter. Meaning I looking for maxima that depend on a parameter.
Here is what I tried to do but FindMaximum is not parametric, so it did ...
1
vote
1answer
24 views
FindMaximum with parametrized NDSolve
I am trying to solve a parametrized ODE, and wanting to find the parameter that maximize the solution at a specific point.
For example, in the following code I am trying to solve the ODE $df/dz=t \...
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3answers
130 views
Why doesn't Mathematica evaluate the series with recursion relationship as expected?
I define a series $dg(i)$ as the $i$th derivative of a function $g[t]$ for $i>0$ and known the first term $dg(1)=(t-x)g(t)$. In mathematica, the code is:
...
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0answers
45 views
Specify direction of propagation in the 1-d wave equation in NSolve and NDSolve [duplicate]
I am solving the 1-d wave equation with the following initial conditions:
...
0
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0answers
33 views
Defining a function through an ODE containing unspecified operators
I want to do some algebra using a function only defined through a DE containing unspecified operators. The DE is
$$
\partial_zu(z) = \left[\hat{D}+\hat{N}(z,u)\right] u(z).
$$
Here $u$ lives in ...
2
votes
1answer
55 views
Using NDEigensystem to find 100 eigenvalues
I'm using "NDEigensystem" to calculate a Sturm-Liouville problem, for which the first 100 eigenvalues are needed. The code is like this:
...
0
votes
1answer
58 views
Plotting basins of attraction of magnetic pendulum in spherical coordinates
I am new in Mathematica, and this is the first time I coding. Following is the code solving differential equations of motions in spherical coordinates of magnetic pendulum and plotting basins of ...
-1
votes
0answers
41 views
Solve the PDE with mathematica
$[\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}]u(x,y)-6[\sin^2(x)+\sin^2(y)]u(x,y)+4.1209 u(x,y)=0$ with the periodic boundary condition $-2\pi <=x,y<=2\pi$. How to write the ...
3
votes
1answer
32 views
NDSolveValue::bcedge: Boundary condition is not specified on a single edge of the boundary of the computational domain
I'm solving a Schrödinger's Equation in 1d, where $\Omega$ is the domain, bcs the periodic boundary condition, init the initial condition.
...
2
votes
1answer
100 views
Problems in running the non-linear PDE system
I'm new to the mathematica and just try to solve an seemingly simply non-lineal coupled PDEs. It is about the diffusion-reaction kinetics in a pellet.The code seems workable, but keep running without ...
1
vote
1answer
54 views
Estimating parameters on system of differential equations
I am looking for some help estimating the parameters of a series of differential equations to assist fitting the experimental data I have collected.
The Problem:
The equations are based off of the ...
0
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0answers
45 views
Analytic continuation of an ODE solution with ParametricNDSolveValue
I am working on the analytic continuation of a solution of the $2\times 2$ system
$$dT=TP,\quad T(1)=Id$$
where $P$ is of the form
$$P=\begin{pmatrix} 0 & t^{-1}\\ \frac{t}{4}+(t-1)^2\left(\frac{r ...
2
votes
1answer
57 views
Describing solution of particular ODE with small parameter
I have differential equation (1) $x''+2\epsilon \nu x'+x+\epsilon x^3=0$. I try to solve it using a method of multiple scales. So $x=x(t)=x(T_0,T_1,T_2,...,T_n)$, where $T_i=\epsilon^i t$.
Then $\...
0
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0answers
44 views
How to Solve a Differential Equation System Depending on Variable Solved in an Implicit Function?
I have an ordinary differential equation system need to be solved by using Mathematica.
$\frac{dk(t)}{dt}=((1-\kappa(t))k(t))^{\alpha}(1-\frac{\kappa(t)}{\kappa(t)+\frac{1-\alpha}{\alpha}\frac{\eta}{\...
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0answers
53 views
How to solve this NDSolve problem in Mathematica?
I found a confused problem in solving a ODE problems with NDSolve in Mathematica, the code is as follows:
I have tried 'Clear[Derivative]' and restart the kernel but these methods don't work.
Here ...
3
votes
1answer
52 views
How to utilize a Pick[] command in a differential equation
The code below is a simplified example of a problem I am working on. I first define a relation V that depends on x[t] and ...
0
votes
1answer
31 views
NDSolve output - ParametricPlot not plotting
I cannot understand why I cannot reproduce an example given in the NDSolve command help.
Namely I would like to plot the steepest ascent path on the surface $z = x^2-y^2$, starting from the point $(0,...
1
vote
1answer
41 views
Context issues when using NDSolve and rule substitutions in a package [duplicate]
I have a .wl package and a demo .nb notebook. The package file is testPackage.wl and it ...
0
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0answers
32 views
Solving a system of equations with a specific shape of the solutions
I have a system of four equations, which are:
...
0
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1answer
39 views
Why is this NDSolveValue function remembering past inputs?
I have been attempting to generate a function that uses NDSolveValue to return the value of a solution to a system of ODE's when an event condition is triggered, as a function of the initial ...
4
votes
2answers
242 views
0
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0answers
37 views
Why do I get a blank graph when using Manipulate with NDSolve?
I'm trying to model an SIR model using the Manipulate function so that I can change the parameters. Although, when I enter in the following code:
...
2
votes
1answer
43 views
Find x at a given t and f(x,t) == constant from a system of coupled PDE
Is it possible to find the speed of a moving front (produced by the below code) in which modulating beta changes the speed of the front?
Basically, I am trying to map the x-values of f(x,t)=0.5 ...
1
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0answers
72 views
Problems with the eigenvalues calculated using NDEigenvalue
I'm trying to solve a Sturm-Liouville problem like
$\qquad -\psi''(z)+(\frac{1}{z}+2\,z)\psi'(z)=\lambda\,\psi(z)$
using NDEigensystem in order to learn how to ...
0
votes
1answer
47 views
Implicit piece-wise function in derivative for differential equation solver
I want to set up a model/simulation that involves numerically solving a set of coupled differential equations, but at some point in time I want some of the variables to quickly jump to a constant ...
1
vote
1answer
78 views
Adding a limit in NDSolve to avoid division by zero
I'm trying to solve a set of differential equations in which one of the functions that describe the time derivative gets values which make it divide by zero
...
19
votes
2answers
2k views
Wrong answer from DSolve when solving a differential equation
Bug introduced in 12.0.0
I was trying to solve the following differential equation: $$\frac{dy}{dx}=x^2+y^2-1 \quad \text{and} \quad y(0)=1$$
and I used the code below:
...
0
votes
0answers
38 views
Manipulate plot of a system of PDEs with NDSolve
Modeling 1D diffusion of an enzyme, e, through a sphere with substrate, s, I arrive at the below equations:
I then pass these equations to NDSolve, Evaluate at a range of r and t and Plot and ...
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0answers
53 views
Why doesn't Mathematica find solution for differential equation when Wolfram Alpha does?
I need to solve differential equation:
dy/dx=tan(1/2*(Pi/2+arctan((|3tan(35*Pi/180)-x|)/(y+3)))), y(0)=0
Wolfram Alpha gives me the output in shape of plot and I need to get the formula used by ...
0
votes
1answer
51 views
Why is NDSolve not working for the given system?
I'm trying to find the solution curves for a system of differential equations. In order to try to complete this task, I've attempted to use NDSolve, but I get an error that says that there are fewer ...
0
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0answers
36 views
DSolve help - List encountered within
I'm reading through a physics paper (it's for the displacement of skyrmions in a 2D lattice) and just wanted a little help in visualizing an equation that is shown:
$$0=\mu \nabla^2\vec{u}+(\lambda +\...
