Questions tagged [differential-equations]
Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
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Differential equations system's solutions differ when one of the constant is 0
I am solving the following system of equations with Mathematica.
$u'=-k_{1}ux+k_{2}x^2, x'=k_{1}ux-k_{2}x^2$
and I obtain the solution for x:
$x(t)=\frac{e^{k_{1}C_{1}(t+C_{2})}k_{1}C_{1}}{-1+e^{k_{1}...
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Problem in implementing periodic boundary condition to solve a system of PDEs with period 2 Pi/constant
I wish to solve the following system of PDEs for h1, h2 using periodic boundary conditions and specified initial conditions. When I execute Mathematica complains that the boundary conditions are not ...
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34 views
3 body problem for earth sun and moon
Im trying to model a 3 body system consisting of the sun, earth and moon.
...
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15 views
System of delay differential equations: using first interpolation as second initial condition
I am trying to solve numerically the following system of two coupled delay differential equations:
$$\dot x(t)=-\gamma x(t)-\frac{\gamma}{4}e^{i\omega_0\tau_1}y(t-\tau_1)\theta(t-\tau_1)+\frac{\...
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66 views
Is Mathematica calculating Lagrangian correctly?
The following Lagrangian is available:
$$
L = (\omega(t))^2J(t,\theta(t))-m(\omega(t))G_gP(t,\theta(t))
$$
Here $\omega(t)$ is the angular velocity of the body; $J(t,\theta(t))$ - a variable moment of ...
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0answers
27 views
Implementing a generic product rule
I'd like to implement a generic rule for expanding differential forms by the product rule. For instance, I'd like to transform the following PDE:
$\phi \frac{\partial \phi}{\partial t} = \phi \nabla^...
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3answers
71 views
How to extract some specific value from NDSolve?
How can i extract some value from NDSolve. We know that gives us a InterpolatingFunction. But i need to use some specific value.
For example this is the NDSolve:
This is the equation used
...
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22 views
Need help with the “step size is effectively zero; singularity or stiff system suspected” message
I'm trying to solve a system of ODEa, and I always get a message saying
NDSolve::ndsz: ..step size is effectively zero; singularity or stiff system suspected.
I tried ...
2
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0answers
37 views
Speeding up the process of NDSolve[] when a user-defined function is involved?
I am trying to tackle a (1+4 dimensional PDE) model at which the solution of the first PDE (with some interpolations and changing the domain) would be used in the second PDE.
In fact, I must choose ...
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2answers
101 views
Non-linear differential equation with tricky variable dependence
My problem regards solving a differential equation and can be reduced to the problem of finding $f(x)$ such that
$\frac{df}{dx}=\frac{dh}{df}$, with $h(f)$ a known function.
I have this list of data,...
7
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2answers
198 views
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Where is the numerical solving breaking down?
I am working with a set of three coupled reaction-diffusion PDEs, and for some parameter values I am getting some not so great solutions. I have been searching documentation and tutorials, and I have ...
2
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1answer
39 views
Does NonlinearStateSpaceModel work with symbolic constants?
I'm trying to put a nonlinear system of two 2nd order ODEs given by:
...
2
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1answer
56 views
Trying to use NDSolve to solve a system of non-linear PDEs representing the development of Alzheimer's disease over time
I'm trying to do something very similar to this question, except with a much larger system of PDEs from this paper. The PDEs are equations 1-18 in that paper. Equations 9, 10 and 15-18 have laplacian ...
2
votes
1answer
61 views
Numerically solving a system of ODEs with parameters [on hold]
I am working on solving a system of coupled ordinary differential equations with initial values given. When I searched about my requirements I got the similar answer here. But I got another condition ...
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0answers
41 views
NDSolveValue::fembdcc: Cross-coupling of dependent variables is not supported in this version
It seems that Mathematica can't solve differential equation when one of the arguments requires that the value of one variable is equal to the value of the other variable, when I try this I get this ...
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2answers
51 views
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NDSolve::conarg: The arguments should be ordered consistently mistake [closed]
I want to solve a system of differential equations, but I get NDSolve::conarg: The arguments should be ordered consistently mistake. How can I avoid that?
code:
...
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0answers
30 views
How to convert this equation to a second order one in f?
This is a third-order differential equation. Is it possible to convert it to a second-order one by integrating it or any other way? I think it could be done by multiplying by some additional factors.
...
4
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1answer
114 views
Solving the Stokes equation for planar Marangoni flow with FEM
Background
I would like to numerically solve the stationary Stokes equation from fluid dynamics
$\eta_i \nabla^2 \vec{u}_i - \nabla p = 0$
with the incompressibility condition
$\nabla \cdot \vec{u}...
1
vote
1answer
59 views
Solution of a system of ODE with Dsolve
I am trying to solve following ODE with Dsolve.
a1[t_] = 2 - 3*Exp[-2*t];
a2[t_] = 1 + Exp[-3*t];
a3[t_] = 4 + Exp[-5*t]
$B=\begin{bmatrix}a1[t] & a2[t] &...
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43 views
Plot a solution of two parametric fuctions [closed]
Please I need Help,
I have the following system of linear differential equations
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1answer
59 views
How to substitute by NDSolve solution to plot a new function
Assume I got some function by NDSolve , like y(t)
...
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0answers
62 views
How to solve this equation in Mathematica?
I wonder what is the best way to solve this equation in MA?
$$ y= \frac{\partial}{\partial x} ~ \frac{\partial}{\partial x^*} f $$
where y and ...
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0answers
95 views
Function value errors in NDSolveValue
I am solving a second order differential equation described by odey below. For the asymptotics, I have the following code which will be used as initial conditions for NDSolve.
...
1
vote
1answer
66 views
Polar plotting Hankel Function with a lot of terms
I am trying to plot a normalized polar plot for the following function with different values of $a$
$$\left\lvert \sum_{n=1}^\infty i^n (2n+1) \frac {P_n^1(cos(\theta))}{\sqrt{\frac{\pi k a}{2}}[-H_{...
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1answer
144 views
How can I get the Green's function of a certain differential equation?
Ho w to extract the green function of the following differential equation. I am trying to extract the analytical form of the green's function.
\begin{align*}
EI_{zz}\,\frac{\partial ^2u\left(x\...
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1answer
80 views
Geodesics in 2+1 Schwarzschild metric
Would appreciate if someone could explain the query that, I am trying to understand the code for timelike geodesic in 2+1 Schwarzschild $(\theta=\frac{\pi}{2})$ where we have taken $M=1$. From this ...
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1answer
24 views
Error when trying to solve a linear differential equation
I am trying to solve a linear differential equation for the change in scale factor term, $\delta a(t)$, when mass terms are introduced to the equations of motion for General Relativity. The first ...
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0answers
29 views
How can I use WhenEvent to stop the integration? [duplicate]
I have a questions about stopping the integration. I calculate the function as the following. It gives the message: "At NN=58.7035438......, the step size is effectively zero; singularity or stiff ...
1
vote
1answer
76 views
Solving these equations with a constraint
I have been for long time now try to solve this equation
q1[t_] = D[x[t], t, t] - 2 (1/y[t]) D[y[t], t] D[x[t], t]
With its complex conjugate
...
3
votes
1answer
54 views
Can Mathematica check ansatz for solutions of differential equations?
I'm just a beginner learning Mathematica. I'd like to do something with it, but I don't know if it is possible.
Suppose I want to solve a system of differential equations, maybe a nonlinear one, and ...
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2answers
82 views
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0answers
57 views
How I can plot Vector3DPlot?
I want to reproduce the vector 3D plots as shown in the figure. It's in spherical polar coordinates (i.e. vector 3D plot on plane).
The angle [Theta] is spherical coordinate is determined by the ...
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41 views
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0answers
56 views
Fail to solve set of PDEs
I tried to solve a[t,z] and u[t,z] from set of PDES.
Here a[t,z] describes laser incident on ...
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2
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1answer
63 views
Laplace equation DirichletCondition ignored
My goal is to find out force between two parallel identical disks with Voltage difference.
To solve this, I tried to use laplace equation.
And below is my code.
where R is radius of disks, d is ...
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0answers
55 views
how to solve nonlinear differential equations which calls other functions that uses states and time as input while solving NDSolve?
I have nonlinear differential equations which require output from other functions and those functions require time and some states as input.
I'm writing the Mathematica code bellow the equation.
$p=...
2
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0answers
53 views
RK4 of second order ODEs system
I'm new here and I have to program explicitly a Runge-Kutta 4 Method for a second order ODEs $10 \times 10$ system: $X''(t)=AX(t)+F(t)$, and the instruction was to make a change of variable $y(t)=x'(t)...
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72 views
Why Mathematica gives this second solution to this first order linear PDE $w_t+3 t w_x=w$?
This is using V12 on windows 10.
I was trying to verify my hand solution with Mathematica. DSolve gives two solutions instead of one, which I do not understand ...
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1answer
83 views
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2answers
53 views
How can I solve this differential equation?
I have a differential equation and when I try to solve it by using the "NDSolve" command, the Mathematica gives an error. The differential equation and error are as follows
...
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55 views
Simplifying a differential equation acting on a product of functions
I have a function $f(x_1, \ldots , x_n)$ in $n$-variables that satisfies a fourth order linear differential equation (say $Df=0$). The function $f(x_1, \ldots, x_n)$ is of the form $f(x_1, \ldots, x_n)...
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34 views
Adding extra species in a model
I am currently working on a model of competition for resources between different species.
I have 6 species competing for 3 resources. The first 3 species start at =0. the 4th species is added at t=...
0
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1answer
69 views
How to chop a complex number?
I'm solving some differential equations by iterating and I want to use Chop to get rid of noice smaller than a certain threshold. However, I found that Chop only "chops" the real part, not the ...
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0answers
41 views
How to solve forward Kolmogorov birth-death equations for unspecified number of populations
I'm attempting to use a forward Kolmogorov differential equation to model a birth-death process. This is fairly trivial when there's only one population, but I'm working with an unspecified and time-...
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0answers
40 views
How to resolve underflow occurrences?
I am solving a second order differential equation described by odey below. For the asymptotics, I have the following code which will be used as initial conditions for NDSolve.
...
0
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0answers
41 views
Non-linear ODE from closed-loop system and Response (Part II)
I again need help with the Mathematica.
We have the following affine system.
I need to get expressions describing the changes of $x_{1} \left( t \right)$ or $x_{2} \left( t \right)$. The only thing ...
0
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1answer
39 views
How to create a correct density plot from “NDSolve” solution?
I would like to create the projection of a solution in plane from the differential equation set solution. However, the way I did it is not as I would like it, it does not have a smoothness.
Here's ...
