Questions tagged [differential-equations]
Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
7,308
questions
0
votes
0
answers
58
views
How to return only the negative complex solutions of DSolve or using FindInstance
I am using DSolve to find the solutions to two differential equations. The problem is from the first solution, I only want the solution that includes a negative ...
- 101
1
vote
1
answer
71
views
Post Processing of Solution and Plot of Coupled Partial Differential Equation Over a Semi-Circular Domain
Linked Question: Solution and Plot of Coupled Partial Differential Equation Over a Semi-Circular Domain.II
Many many thanks to @Nasser (https://mathematica.stackexchange.com/users/70/nasser) for his ...
- 87
0
votes
0
answers
54
views
Stiffness or singularity in NDSolve for a system of equations with switchpoint
I am trying to solve the following set of equations:
...
- 73
2
votes
1
answer
100
views
Solution and Plot of Coupled Partial Differential Equation Over a Semi-Circular Domain.II
This question is connected with reference to my previous question (Solution of Dimensionless Partial Differential Equation Over a Semi-Circular Domain), where I asked for a help to solve the following ...
- 87
1
vote
0
answers
48
views
Why this code does not show three legend lines?
My code shows empty legend lines. What should I do to show the graph with three legend lines?
...
- 11
1
vote
1
answer
98
views
NDSolveValue result contradicts initial condition
I'm trying to solve the Schroedinger equation in a box with two holes defined by:
...
- 13
2
votes
2
answers
166
views
1
vote
1
answer
79
views
A way to generalize my code for this non linear ODE problem
I am trying to solve the differential equation $y''(x) = y(x)+\sin[y'(x)]$ using "Fixed Point Iteration" over the interval $[0,1].$ Now using central difference method I arrived at the ...
- 143
1
vote
1
answer
58
views
Adding symbolic functions and manipulating results of DSolve
I want to add a symbolic function and its second derivative.
The symbolic function is given by DSolve:
...
- 13
4
votes
2
answers
207
views
Solution of Dimensionless Partial Differential Equation Over a Semi-Circular Domain
My problem is to solve the following BVP.
and I want to recreate a contour plot like the following graph using Mathematica.
I am trying with the following code.
...
- 87
3
votes
1
answer
122
views
Solve Differential Equation Numerically
I investigated my system and encountered differential equation such as
$y''(x) = e^{y(x)}-e^{-2y(x)}-e^{y(x)-y(x+d)}$,
where $d$ is a constant. The boundary condition is
$y'(0) = 30$
$y'(\infty)=0$.
I ...
- 33
1
vote
1
answer
78
views
Solve dimensionless PDE in polar coordinate over a semi-circular re
I am trying to solve the following BVP in mathematica
using the following code:
...
- 87
1
vote
0
answers
249
views
+500
How can I solve unintegrated Boltzmann equation fast and robustly?
Consider the following integro-differential equations (the unintegrated Boltzmann equations for ultrarelativistic particles in expanding Universe):
$$
\left(\frac{\partial}{\partial t} - H p \frac{\...
- 4,984
1
vote
1
answer
77
views
A code for producing system of equations for central difference method
I am trying to solve the differential equation $y''(x) = y(x)+\sin[y'(x)]$ numerically over the interval $[0,1].$ Now using central difference method I arrived at the equations of the type
$$ y_k = \...
- 143
0
votes
1
answer
72
views
Solving differential equation with hyperbolic functions
I've been trying to solve the following differential equation:
\begin{equation}\left( \frac{d \tau}{d \sigma} \right)^2 = \frac{(E_0 \cosh\sigma-p_\tau\sinh\sigma)^2}{(E_0 \cosh\sigma-p_\tau\sinh\...
- 47
0
votes
0
answers
110
views
Iteration show different values in solving a pde in mathematica
I have a pde given below:
$u_{t}-u_{xx}+\frac{1}{4}u=0, $
with boundary conditions
$u(0,t)=1,\ \ u(1,t)=\frac{1}{2}e^{\frac{-t}{4}}+e^{\frac{-1}{2}},$
where $0\leq x\leq 1$. If the initial iterate is $...
- 53
0
votes
1
answer
97
views
How to plot a differential equation?
I solved a differential equation, which gave me the result:
-R[x]*Sqrt[(Q/R[x]) - 1] - (Q/
2) ArcTan[((2 R[x] - Q)*Sqrt[(Q/R[x]) - 1])/(2 R[x] - 2 Q)] == -a*x
...
- 103
0
votes
1
answer
46
views
Labelling vector state variables for solution of system of ODEs
This might be a duplicate, but I have not seen this problem addressed for DSolve usage.
I have a system of ODEs of the form
Y' = AY + B
When we put this into Mathematica as a vector variable:
...
2
votes
1
answer
67
views
FEM solution for onedimensional boundary value problem doesn't evaluate [closed]
modified
Based on this, unfortunately closed, question How can we know on how many parts is domain splitted with MaxCellMeasure? [closed] I would like to know why ...
- 47.2k
0
votes
1
answer
65
views
How to force Wolfram solve the ODE with respect to h[s]?
I have a problem with the DSolve operator. It just gives me the initial ODE as an answer, however, obviously, I need to find the answer h[s] as a function of f[s] and its powers (or whatever else). It ...
0
votes
1
answer
52
views
How to reduct the terms of differential equation?
How can one bring the terms of a differential equation below to a standard form with coefficients before h[s], h'[s], h''[s] and their powers?
Or, better, can someone help me with solving it with ...
0
votes
0
answers
43
views
2
votes
1
answer
85
views
Mathematica thinks that an initial condition is a boundary condition
I would like to solve the following reaction-diffusion problem in Mathematica using NDSolve:
...
- 21
1
vote
1
answer
48
views
Plotting Dengue Infection Prevalence Sensitivity to Biting Rate Variations
I want to explore how varying values of the biting rate affect infection prevalence in humans in our modeled dengue outbreak, keeping all other parameters constant.
I provide you the code that I use ...
0
votes
2
answers
81
views
Set of differential equations with trigonometric functions and a derivative squared
I've been trying to solve a set of differential equations that involve the square of a derivative, similar to another post I made here, and trigonometric functions, as seen here
\begin{equation} \frac{...
- 47
4
votes
1
answer
66
views
Modeling Infection Spread among Different Age Groups with Contact Matrix
In this code, we divided the population into children, adults, and old people.
The probability of infection per contact, $b$, is 5 % for people of all ages
The total population size is 1 million, and ...
7
votes
2
answers
585
views
The Poincaré Sections of Yang-Mills-Higgs System [closed]
In the papers Quantum Chaos in a Yang-Mills-Higgs System and DIFFERENT FACETS OF CHAOS IN QUANTUM MECHANICS, the authors have plotted three Poincaré sections for different values of ...
- 1,502
0
votes
1
answer
86
views
Evaluation and plot the result of NIntegrate obtained from NDSolve
First I solved coupled ODE using NDSolve. Now I want to integrate the expression (p'''[0] - ((1.0/k)*p''[0]) + (beta*m*m*s[0]) with respect to the parameter ...
4
votes
2
answers
435
views
Solving coupled differential equations involving the square of the derivative
I want to solve the following system of coupled differential equations in order to obtain particle trajectories:
\begin{equation} \frac{dt}{ds} = (E-y\, p_t)y \end{equation}
\begin{equation} \...
- 47
1
vote
3
answers
164
views
Solving Geodesics from Christoffel Symbols
I am somewhat new to using Mathematica and I am facing difficulties with a specific problem related to the geodesics of Einstein's field equation in a vacuum.
The metric I am working with is derived ...
- 11
0
votes
1
answer
63
views
How can I obtain the temperature profile from a pressure profile of a partially filled rotating cylinder?
I would like to plot the temperature profile of a partially filled rotating
cylinder. However, I am only familiar with how to plot pressure profiles. Can you
please suggest a method for deriving the ...
- 1,025
0
votes
0
answers
79
views
Plot the Integration of an expression that uses the results of NDSolve
I want to plot the Integration of an expression that uses the results of NDSolve. But I am getting a blank window from the following code.
...
1
vote
1
answer
135
views
Plot the evaluated results of NDSolve [closed]
I am trying to get a plot of dpdx vs x using the following code. But I am getting a blank window.
...
1
vote
1
answer
75
views
What are some ways to speed up calculations
Below is the code for calculating the eigenfunctions and eigenvalues of the following system:
$HC[u(\rho,z)]=-\frac{1}{2}\Delta u(\rho,z)-\frac{1}{\sqrt{\rho^2+z^2}}u(\rho,z)+\frac{B^2}{8}\rho^2 u(\...
- 1,731
0
votes
1
answer
77
views
Why does DSolve show result as {}? [closed]
Using the following code, I get as an output: {}.
Does anyone know what does that means?
...
1
vote
2
answers
80
views
Axisymmetric cylindrical Laplace's equation with a boundary condition at infinity
I'm trying to solve Laplace's equation in cylindrical coordinates. The solution is axisymmetric and also symmetric with respect to the $r=0$ plane. Hence I only care about solving in one quadrant. The ...
- 35
0
votes
0
answers
38
views
Plotting NIntegrate result obtined from NDSolve
I am trying to get a plot of x vs dpdx when - 0.5 < x < 0.5 which uses the results of NDsolve and F vs delp when -2<F<2.
...
2
votes
2
answers
155
views
How to numerically solve symmetric top with fixed point motion equations with Mathematica?
I am trying to numerically solve the equations associated with the motion of a symmetric top with a fixed point. Details about this system can be found in Goldstein's Classical Mechanics book (3rd ...
- 953
1
vote
0
answers
38
views
Is there documentation for "FeynmanKacFormula" under "ItoProcess"? [closed]
Under the command ItoProcess there are "Properties related to ItoProcess" and one is "FeynmanKacFormula". Where can I find documentation on this?...
- 141
2
votes
1
answer
57
views
Plot several graphs of a function density distribution using Table
I would like to plot the density distribution graphs of the eigenfunction en[B][[2, 1]] when a parameter B is changed.
But the ...
- 1,731
3
votes
1
answer
114
views
Second order Poisson ODE
I have a 2nd differential Poisson equation for the electric field in a semiconductor (application for a MOS simulation, hopefully).
I have the formula:
with the condition that after a certain value(...
1
vote
1
answer
78
views
NDSolve problem with conservation laws
I am not an experienced Mathematica user, but decided to use it this time because of the in-buit special functions that it has.
My problem is a solution of the following ODE
...
- 111
0
votes
0
answers
34
views
ParametricNDSolve with known solution at one limit
The ODE I wish to understand is the following:
...
- 155
2
votes
1
answer
78
views
Need help solving cylindrical Laplacian
I'm trying to solve the cylindrical Laplacian for a heated disk in a large cylinder. The cylinder and disk have constant temperatures and I only care about the temperature field between the disk and ...
- 35
0
votes
0
answers
44
views
ODE of HJB function
I want to solve the following ODE where W is a function of x. Any suggestion? Thank you!
...
- 1
4
votes
3
answers
100
views
How do I get a coefficient matrix from a second order ODE's system?
I got this system:
I need to transform this ODE system in a matrix form, because I need to evaluate its stability and, further, plot the eigensystem with the Stream Plot function.
Is there any ...
0
votes
0
answers
60
views
Plotting phase portrait for second order ODE(which has no analytical solution)
I'm trying to plot $ y(t) $ against $ y'(t) $ (phase portrait) for the following ODE:
$$ y''(t) + y(t)+9.8*sgn(y'(t))=0 $$
where all derivatives are with respect to $t$. Due to the presence of the ...
- 33
0
votes
0
answers
42
views
WhenEvent in ParametricNDSolve but not executed
I tried to solve a partial differential equation with parameters, the critical condition of which I used WhenEvent to express, but the solution after bringing in the parameters shows that the ...
- 1
2
votes
1
answer
91
views
SIR Parameter Estimation in Mathematica
All infected individuals go through an incubation period, which lasts on average for 4 days. During this time, individuals are not infectious, nor do they have any excess mortality risk.
All infected ...
4
votes
2
answers
111
views
NDSolve is not picking the correct initial condition
I am solving a differential equation in mathematica:
...
