Questions tagged [differential-equations]
Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
4,529
questions
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Swarming on Riemannian Manifolds
I am working on a swarm project on robot operating system,
the control structure of the project is on page 32. Technical implementation is also available on page 32. I have successfully run it.
This ...
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0answers
18 views
NDSolve and equations of motion
I am trying to use NDsolve to solve a set of coupled second order ODEs. Here are the initial conditions:
...
-1
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0answers
30 views
One dimensional wave equation [on hold]
The sermon about the one dimensional wave equation is, that all solutions have the following form (to simplify we include the velocity into time t'= c t):
$$ u_{t t} - u_{x x} = 0 $$
$$u(x,t)= F(x+...
1
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1answer
53 views
NIntegrate over regions, FiniteElement options
I am using NIntegrate to integrate a 3-dimensional region. When I don't set any integration options, I get a warning
The global error of the strategy GlobalAdaptive has increased more
than 2000 ...
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0answers
25 views
How to get the NDSolve to seek only a real solution?
I use NDSolve to solve system of 2 ODE of 1st order:
...
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0answers
49 views
Solving time dependent boundary conditions heat PDE
I am attempting to solve the heat equation $\frac{\partial T}{\partial t}=\nabla^2T$, where $T=T(x,y,z,t)$, subject to the following boundary conditions:
$\frac{\partial T}{\partial x}|_{x=10}=\frac{\...
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0answers
36 views
Could you help me convert my PDE into a boundary value problem?
This is my code. It works as an initial value problem, but I want to solve it as a boundary value problem.
...
0
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1answer
39 views
NDSolve::deqn: Equation or list of equations expected instead of eqns in the first argument eqns
I am new to Mathematica, actually, I am working on a project based on Swarm Intelligence. I am trying to run a simulation of sphere formation of 10 robots, but there is a problem in equations. Here is ...
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0answers
25 views
Solving PDE with boundary condition (laplace equation)
I am wondering if Mathematica can solve the below PDE. Could somebody please help me?
...
8
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2answers
113 views
1DPoisson equation with Dirac delta
I was writing my own FEM method to solve the Poisson equation
\begin{align}
-u'' &= \exp(-c(x-1/2)^2)\\
u(0) &= u(1) = 0
\end{align}
where c=100.
and I'm reading from the book of Mats G. ...
0
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0answers
41 views
Brusselator Model - solution and graph [on hold]
I am trying to solve the Brusselator differential system and plot the solutions but I have a problem with DSolve - it doesn't give any result after a couple of ...
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1answer
41 views
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1answer
46 views
Using the results from NDSolve in another equation
I want to use the results sol returned from NDSolve (values of f at different ...
2
votes
1answer
61 views
Using GreenFunction in 2D free space for Laplacian
V 12. on windows.
I have a question about using Mathematica's GreenFunction to verify known result for Green function for Laplacian in 2D. (I also have question ...
2
votes
1answer
65 views
More elegant/efficient numerical WKB implementation for 1D Schrödinger Equation
I'm trying to figure out a better way to implement numerical WKB quantization of a spectrum. WKB quantization is the condition that
$$\oint_{E}p \, \mathrm{d}q = \pi \hbar (n+1/2)$$
So the idea to ...
0
votes
1answer
57 views
Allow Mathematica to solve the differential equations with larger than 16 digits parameters
Consider the system of differential equations
...
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0answers
20 views
Defining second derivative boundary condition using DEigensystem
I tried to solve a fourth-order eigenvalue problem with boundary conditions on high order derivative.
For example, the following equation,
with a homogenous Direclet condition at the edges and a ...
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53 views
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24 views
Using assumptions in DSolve
I want to solve the following differential equation
DSolve[u'[\[Xi]] == a u[\[Xi]]^(2 - m) + b u[\[Xi]] + c u[\[Xi]]^m,
u[\[Xi]], \[Xi]]
with the assumpetion
...
5
votes
2answers
114 views
Error trying to solve a 2D elasticity problem using FEM package
I have the following equations
$$\frac{\partial{N_x}}{\partial{x}}+\frac{\partial{N_{xy}}}{\partial{y}}=0$$
$$\frac{\partial{N_y}}{\partial{y}}+\frac{\partial{N_{xy}}}{\partial{x}}=0$$
where
\begin{...
5
votes
1answer
71 views
Eigenvalues and numerical eigenfunctions for similar differential operators
I am looking to numerically approximate the eigenvalues and eigenfunctions for a differential operator I am working with, assuming $\pi$ periodic boundary conditions.
Namely, I define the function $...
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0answers
24 views
Biot_Savart law for bounded current systems [migrated]
I have a PDE I don't know how to solve, which is a result of a physics problem related to the Biot-Savart equation. The PDE in question is an equation for B:
curl(B)=del(phi)
where phi is a known ...
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1answer
49 views
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0answers
48 views
Help with DSolve using exact Mathematica System
In an attempt to error-trap a 3-D DSolve solution, resorted to an eccentric circle flat model (analog to non-geodesic circles on a sphere), for which the following is an abridged code :
...
2
votes
0answers
104 views
Solving for a minimum action path in mathematica
I am interested in computing a quantity that is mathematically defined as follows,
$$\phi(x_1,x_2) = \inf_{T>0} \inf_{\gamma \in C^{x_2}_{x_1 }(0,T)} \int_{0}^T L(\gamma, \dot{\gamma})\mathrm{d}t$$...
1
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1answer
47 views
How do I solve a large system of differential equations with indexed functions?
I strongly suspect that matrix methods are the right answer here, but I am having trouble visualizing how to set it up. Imagine a large number of coupled functions:
...
4
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0answers
36 views
NDSolve`ProcessEquations inside Manipulate
NDSolve and NDSolve`ProcessEquations can handle equations with vectors on each side like this one:
...
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0answers
112 views
Need help with ParametricNDSolveValue for ODE with two variables and Do-loop
I' m trying to solve a tricky 2-nd order ODE with
ParametricNDSolveValue for boundary conditions (BCs) y = 0 at R and ...
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0answers
49 views
Basic Question: How do you represent simple equations of motion in Mathematica? [closed]
I'm trying to set up a simple sandbox to understand motion. First I want to represent linear motion in Cartesian coordinates, then in polar. The first step is a set of equations that represent ...
1
vote
1answer
73 views
Strange results from NDSolve after using a smooth (Tanh) function to approximate a discontinuous (jump) event
I am solving a system of ODE which contains a discontinuous ode (the equation v[t]== ...in the following code and it means that my ...
1
vote
1answer
51 views
Export the list of value for the system of equation in the Loop using NDSolve
I want to solve a system of ODEs in sweeping a parameter $\omega$, and in that final conditions need to be carried for the initial condition for the next value of parameter $\omega$. Also, I want to ...
0
votes
1answer
40 views
Seting a function with NDSolve
I want to set a function sg which is a solution of the NDSolve based on a position x, time t ...
1
vote
0answers
90 views
Numerical integration of damped wave equation
I am trying to solve the equation
$$ \frac{d^2u}{dt^2}-\frac{d^2}{dx^2}\left(c_s^2u+\nu\frac{du}{dt}\right)=0 $$
with initial conditions
$$u(x, 0)=0$$
$$\frac{du}{dt}|_{t=0}=0$$
and boundary ...
3
votes
1answer
127 views
Solve a one dimensional heat transfer problem with NDSolve
The following problem is a 1-D heat transfer conduction problem:
where,
I am trying to solve with NDSolve like this way:
...
0
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1answer
117 views
3
votes
3answers
102 views
Constraint of NDSolve with an integral of the solution
I'd like to use NDSolve and to make a constraint with an integral.
For example, take the very simple : $$f'(x)=-f(x)/x_0 $$
the solution is $$f(x)=f_0 e^{-x/x_0} $$
And $f_0$ is given by : $$\int_0^...
2
votes
2answers
86 views
NIntegrate failed to converge and why?
i have put up and question about the NDSolve and have got the solution of the ODE,and also got the figure of t1-t ,however when ...
4
votes
3answers
147 views
NDSolve will try solving the system as differential-algebraic equations but it didn't get the solution
Please help me deal with this kind of question about ODEs.
My codes are as follows
...
1
vote
1answer
38 views
Confusing behavior of LQR control that strongly depends on system output (with odes solved by NDSolve)
I am implementing a LQR control of a 3-floors structure.
Firstly, I obtained a reasonable result with my first code (Code 1 as shown below). In this code, the ...
1
vote
1answer
48 views
Visualizing a system of differential equations [closed]
I have the following system of differential equations:
x'[t] == x[t] - x[t] y[t]
y'[t] == x[t] y[t] - y[t]
I use this Wolfram Mathematica code:
...
1
vote
1answer
86 views
Bifurcation diagram
I have a differential equation
y''[t] + 0.3*y'[t] - y[t] + (y[t])^3 == A*Cos[114.14*1.2*t]
with
y'[0] == 0, y''[0] == 0
t varies from 0 to 1500,
A varies ...
1
vote
1answer
35 views
1
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1answer
52 views
How to address an element of variable vector for coupled system of ODE while using NDSolve
I am using Mathematica from around 10 months. I want to solve numerically a system of equations with number of equations more than 35 to 40. System of equations is shown below for small number of ...
5
votes
1answer
53 views
Why does this stiff BVP return unevaluated but a similar IVP produce a solution?
In Solving a steady-state viscous Burger's equation with NDSolve, one question involves the following problem:
...
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0answers
62 views
Solve ODE system efficiently with mathematica
I've been trying to solve a system of ODE's with mathematica, which is a master equation of a hierarchically organized tissue model, where I want to quantify the number of cells at level 'k' with 'm' ...
2
votes
0answers
108 views
Nonlinear, second order system of ODEs not solved by Mathematica, solution however exists
I am currently working on solving a system of two coupled nonlinear second order ODEs.
I have already shown by hand, that 2 real solutions, as polynomials of second order, exist but I want to use ...
0
votes
1answer
161 views
Need help on working with parametric function
Here is an ODE solved by ParametricNDSolveValue solver.I got the solution.
Now, I need to solve these two equations:
p1 = 10 h - l;
p2 = 10 h1;
where ...
6
votes
2answers
193 views
Solving a steady-state viscous Burger's equation with NDSolve
A steady-state viscous Burger's equation is given by
$$ u\,u'=\nu \,u'', \quad x\in (-1,1), $$
$$ u(-1)=1+\delta,\quad u(1)=-1.$$
Here $\nu>0$ is the viscosity, $\delta>0$ is a small ...
1
vote
0answers
45 views
Solve the Schrödinger equation of a RF-SQUID
I'm trying to solve a time-indipendent Schrödinger equation. This is the Hamiltonian:
$H=E_Cq^2-E_J\cos(2\pi\varphi)+\frac{E_L}{2}\varphi^2$
(assume $E_C=1$) where $q=-i\frac{d}{d\varphi}$ and:
$U(\...
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solution of a coupled differential equation with variable
I have written a code of a set of a differential equation and for one of the variables in the differential equation I have written set of another differential equation how should I call it in the ...
