Questions tagged [differential-equations]

Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.

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1answer
73 views

“Fewer dependent variables than equations, so the system is overdetermined” without any BC's

Consider this system of PDEs. eqn1 = D[u[x, t], x] + 5 D[u[x, t], x, x] + D[v[t], t, t] - 4 == 0 eqn2 = D[v[t], t] + D[u[x, t], t, t] + v[t] == 0 I would like to ...
4
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1answer
102 views

Solving Laplace's equation in 2D using region primitives

I was looking at examples of solving problems in electromagnetism and ran across this question, which was a great example of just that. However, looking at the Dirichlet condition, both answers define ...
1
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1answer
41 views

NDSolve with Events that reevaluate with different Discrete Variables

I have the following problem: I have a set of ODEs and some discrete variables which I can solve successfully. Now I want mathematica to check at every $0.1 \,t$ time step, wether it would increase ...
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69 views

A system of linear differential equations with variable (time-dependent) coefficients

I have searched almost all similar pages discussing a system of differential equations, but none of them discussed the case of variable coefficients. My problem is a bit more complicated, because ...
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0answers
78 views

find ODE solutions and suitable initial conditions to get solution

DSolve[2.56 x''[t] == -0.32 x'[t] - x[t] - 0.05 x[t]^3 + 2.5 Sin[t], x[t], t] I want to find the solution and find two initial conditions such that their ...
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2answers
81 views

Manipulate NDsolve 1D-reaction diffusion equation

I want to solve the following 1D-reaction diffusion equation: $$\frac{\partial}{\partial t}u(t,x)=\alpha\,\frac{\partial^{2}}{\partial x^{2}}u(t,x)+a\,u(t,x)$$ $$u(t,0)=0\,\,\,\,\,\text{et}\,\,\,\,\,u(...
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64 views

Fit a three-pulse sequence

I am wondering how to properly fit the three-pulse sequence shown below. I have tried a method which is fitting the three pulses with three polynominal functions seperately and then finding the x-...
1
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1answer
74 views

solving coupled differential equations

I am solving 6 differential equations in matrix form as: ...
3
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1answer
101 views

Solving Piecewise Differential Equation using NDSolve (coupling at BC)

I am having some issues in dealing with a system of differential equations. I would like to solve a 1D diffusive heat equation across several regions with different material properties. I now have a ...
1
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1answer
88 views

Solving Nonlinear Heat Equation with initial Conditions

I have the following setup for the linear heat equation on an infinite rod (see below). This is a pretty standard setup and the initial condition is $e^{-x^2}$. This initial condition is not special, ...
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0answers
79 views

Ways to decrease computational time

I have created a 2D axisymmetric simulation of the motion of charged particles in an electric field. The electric field is created by a needle attached to a top plate both of which are at -3800V with ...
0
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1answer
133 views

Solving a Reaction-diffusion system

I'm just a beginner in Mathematica software. I have version 12. I am looking for a program that will solve a prey-predator system with diffusion. My problem is that I tried a previously posted ...
3
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2answers
82 views

Extracting data from InterpolatingFunction 2D surface plot

I would like to directly extract the surface plot data from the solution to a differential equation (using NDSolve). While there are many examples of this I haven't been able to find an example in 2D. ...
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59 views

NDSolve with Functions Depending on time and time dependent Functions

EDIT: following the advice of using Raw Input Form, the equations have the following form ...
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0answers
56 views

Plotting PDE Solution With Changing Parameter

I have a Fokker-Plank equation I'm trying to solve the Fokker-Planck equation $$\frac{\partial p}{\partial L}(L, \eta)= \frac{1}{L_{loc}}\frac{\partial}{\partial \eta}\left[\left(\eta^{2}-1\right) \...
4
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1answer
127 views

How to get DAE representation from equations?

Update2: Thank you for all of your answers. I would like to clarify the question as I did a bit of research on DAE representations and their applications in software. There are 2 representations used ...
3
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1answer
247 views

2D Oseen equations

Background info: https://en.wikipedia.org/wiki/Oseen_equations ...
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1answer
71 views

Parametric plot of data from NDSolve

I have been trying to plot the solution of a set of differential equations solved used NDSolve. Now, in one of the cases, I have the find a parametric plot of the ...
5
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1answer
140 views

NDSolve::femcmsd: The spatial derivative order of the PDE may not exceed two

I was in the impression that V12 can now handle higher order PDES but for this particular case it fails to produce any solution. ...
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1answer
65 views

Plot a family of solutions of ODE with singularity

In the post Use Mathematica to plot the flow of an ODE with discontinuity, the following ODE with discontinuous coefficient was solved ...
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2answers
52 views

Delay in the beginning of solution for two ODEs

I have two couple ODEs and the second one has a delay in the time for starting. I mean, the first ODE starts at t=0 and the second one at t=20. How can I solve the second one in the correct time ...
2
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0answers
101 views

Model 1D Vlasov Equation

Vlasov Equation The non-relativistic form of the Vlasov equation is given by: $$ \partial_{t} f\left( \mathbf{x}, \mathbf{v}, t \right) + \mathbf{v} \cdot \nabla f\left( \mathbf{x}, \mathbf{v}, t \...
3
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1answer
102 views

Solution of convection dominated PDE with conditions only on the interior of the domain

I'm Trying to solve the following PDE: $$ \frac{1}{20}\left(2 x_1^2+x_2^2\right) -25\left( \begin{bmatrix} 0\\ \frac{6 \cos(x_1)}{-37 + 3 \cos(2 x_1)} \end{bmatrix}^\intercal \nabla_{x_1,x_2}V(x_1,...
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0answers
41 views

How to use Parallel computing on Manipulate option on ParametricNDSolveValue

My aim is to use Manipulate option on the ParametricNDSolveValue. When ever i run my code "Manipulate" option runs very slow and some time shows Aborted when check for that value of parameter it works ...
6
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1answer
240 views

Solving ODEs vs VoronoiMesh

I'm using VoronoiMesh to model cells in an epithelium. The concentration of certain proteins within the cells are determined by solving a system of ODEs per cell. ...
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1answer
108 views

1d coupled field PDE in MMA

how can we correctly solve 1d coupled field pde in MMA 12? Description for the problem: the article the phase field fracture model in one dimension I have proposed the following code (based on the ...
2
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0answers
93 views

NDSolve and DSolve solutions

Sorry for this probably trivial question, but I'm at a loss with this simple problem and the way Mathematica handles it. It's about a free-falling object, dropped by a height of 10, starting with zero ...
5
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1answer
81 views

I can't get DSolve to work on coupled equations

In trying to solve a geodesic equation, I have these coupled equations: ...
3
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1answer
89 views

How to solve Parabolic partial differential equation

I have the following differential equation $\frac{\partial u}{\partial t}=\nu \frac{\partial^2 u}{\partial y^2}$ where $u=u(y,t)$ with boundary and initial conditions: $\mu\frac{\partial u(0,t)}{\...
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0answers
99 views

Using NDSolve for differential equations

I'm trying to numerically solve the following differential equations eqs for plotting the bifurcation diagram. However, under special values of the parameter u, I get a problem when calculating the ...
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0answers
96 views

Determining the price of an option using Black-Scholes

Code for randomly generated interest rates: ...
7
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1answer
131 views

How to combine NDSolve interpolating functions?

In the following working example ...
0
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1answer
136 views

How to create an animation of charged particles' motion in an electric field

I am trying to create an animation of 3 particles' motion in an electric field. The electric field is created by a needle attached to a top plate both of which are at -3800V with a grounded plate ...
2
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1answer
40 views

Plot solution of ODE with singularity

I wish to plot the solution of the following ODE: ...
6
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1answer
313 views

How to speed up NDSolve when there are ~400k equations?

I'm trying to use NDSolve to solve a set of ~400k equations. The problem I met is: when I ran the evaluation, Mathematica (version 11.0) raised an error: ...
7
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1answer
189 views

Nonlinear elasticity PDE in Mathematica 12

Mathematica 12, Windows 10. I am trying to solve a PDE in one spatial dimension $R$ and time $t$. I need a solution for displacement $r(R,t)$, radial Cauchy stress $T_{RR}(R,t)$, and radial growth $\...
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49 views

Singularity in my system of differential equations causing problems for NDSolve

I have the following differentials equations, with the corresponding initial conditions: ...
9
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1answer
342 views

Deep learning outperforms in symbolic integration and ODE?

There comes a new paper on arXiv (arXiv 1912.01412, Deep Learning for Symbolic Mathematics by Guillaume Lample, François Charton) claiming that a deep learning model outperforms Mathematica a lot in ...
6
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1answer
75 views

How to help NDSolveValue handle the addition of another dependent variable in a set of reaction-diffusion equations

I am trying to use NDSolveValue to solve a system of coupled reaction-diffusion equations in a 2D space (technically 3D cylindrical coordinates, but due to radial ...
2
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1answer
81 views

System model merge with multiple input and one output

I was curious, and I used the built-in functions of Mathematica to analyze the following scheme: I used SystemModelMerge as: ...
1
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1answer
50 views

Using Grad and NDSolve with vector variables

A simple orbital model might be developed like this: ...
3
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1answer
60 views

NDSolve Stiffness and Strange Behaviour with Dirichlet Conditions

I working with the following semiconductor potential equilibrium equation for a diode $$\psi(x)''=e^{\psi(x)}-e^{-\psi(x)}+10^6\text{sgn}(x-(l+r)/2)$$ where $l$ and $r$ are left and right boundaries ...
1
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1answer
96 views
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61 views

solve a differential equation numerically

I have to solve numerically an equation of the form ...
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0answers
130 views

How to solve ode with convolution?

my question is as this and i want to get the solution of this ode x(t) $ ({M_{33}}{\rm{ + }}{{\rm{m}}_{33}})x''(t) + \int\limits_{ - \infty }^t {x'(tau){K_{33}}(t -...
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0answers
66 views

Phase portrait of n-dimensional state-space system

It is usually not difficult to study the state space for n = 2,3 variable states. What if these variables are more than 3, for example 4,5 or 6? There is a rule according to which the dynamic features ...
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2answers
57 views

solve a matrix differential equation numerically [closed]

I want to solve numerically a differential equation like iy'[t]=y[t]/20 where y is a 2*2 matrix and i is iota. Please suggest me a way to proceed.
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0answers
35 views

Boundary value problem using DTM-Pade

I have written the following code for solving a boundary value problem using DTM-Pade, but it is consuming a lot of time to execute. Can someone help me in rectifying the error in the code (if any) or ...
2
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2answers
119 views

Error test failure when solving two coupled ODEs

by NDSolve; this is work until y=6.22 ...

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