Questions tagged [differential-equations]
Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
4,662
questions
2
votes
1answer
47 views
Plotting a two parameter function evaluated at a specific point
I am trying to solve the following problem: given the differential equation $$\frac{d^2y}{dx^2}+\bigg(a+b\frac{2}{\pi}\tan^{-1}x\bigg)y=0$$
subjected to two different initial condition we get two ...
0
votes
0answers
34 views
DSolve function is not working for Hypergeometric Function
I am trying to get the solution of second order differential equation, but it is not working. Any idea about it will help me a lot.
...
1
vote
1answer
33 views
Error message when trying to solve 2 coupled PDEs using NDSolve
I'm currently facing a problem when trying to solve 2 coupled PDEs. I get the warning messages:
NDSolve::fembdcc: Cross-coupling of dependent variables in DirichletCondition[IPF==IPB/10,z==5.] is not ...
0
votes
0answers
17 views
NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0 [closed]
sol = NDSolve[{y''[x] == -(9.8/5)*sin[y[x]], y[0] == 25 Degree ,
y'[0] == 0}, y, {x, -10, 10}]
0
votes
0answers
36 views
Error while giving initial condition in NDSolve [closed]
I am trying to solve following differential equation
$$\frac{d^2y}{dx^2}+(a+b \frac{2}{\pi}\tan^{-1} x)y=0$$ with the initial condition $y(-10)=e^{10i\sqrt{a+b}}$ and $y'(-10)=-i\sqrt{a+b}e^{10i\sqrt{...
4
votes
1answer
35 views
Nonlinear differential equation with unknown parameter and integral form boundary condition
I'm trying to solve numerically a non-linear problem in order to determine the velocity field ($U$) and the film thickness ($h$) of a non-Newtonian fluid over an inclined plane. The equations are,
$$\...
3
votes
1answer
95 views
Why can't MMA solve this system of differential equations?
This system of differential equations can be solved in order to
obtain the expression of x[t] y[t] z[t]
...
2
votes
1answer
49 views
Maximizing Output from ParametricNDSolve
Given a system of differential equations that are dependent on two parameters, such as the system below (the equation below is not that important, I am interested in a general procedure given a ...
1
vote
0answers
31 views
Unexpected stiff system error [closed]
Let there be the following functions
ya[t_, x_] := Cosh[t*x]
za[t_, x_] := Sinh[t*x]
wa[t_, x_] := x*Sinh[t*x]^2
One can verify that the following PDE's hold
<...
0
votes
0answers
42 views
Heat transport with Neumann bc in older Mathematica versions [duplicate]
Im trying to solve a simple heat transfer equation: $\partial_t T-\beta \partial_{xx}T=0$ for a finite system $x\epsilon <0;L>$ along with initial/boundary conditions:
1) $T(x,t)=0$ for $t<...
1
vote
1answer
58 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
votes
1answer
96 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
vote
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 ...
0
votes
0answers
66 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 ...
1
vote
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 ...
-2
votes
2answers
79 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(...
0
votes
0answers
62 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-...
0
votes
0answers
27 views
Using VariationalD on previously defined functions [closed]
Do you know whether there is a way to get around the following problem?
Say we define a very simple function:
f[t] = 2 y[t]
and want to use the ...
0
votes
0answers
43 views
Getting error message from WhenEvent in NDSolve [closed]
I'm using this code; I would like to find the value of tmax such that a certain condition is satisfied.
...
1
vote
1answer
66 views
3
votes
1answer
94 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
vote
1answer
73 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, ...
0
votes
0answers
75 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
votes
1answer
124 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
votes
2answers
74 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.
...
0
votes
0answers
57 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
...
1
vote
0answers
51 views
Plotting PDE Solution With Changing Parameter
I have a Fokker-Plank equation
I'm trying to solve the Fokker-Planck equation
$$\frac{\partial p}{\partial L}(L, \eta)= \frac{1}{L_{loc}}\frac{\partial}{\partial \eta}\left[\left(\eta^{2}-1\right) \...
4
votes
1answer
115 views
How to get DAE representation from equations?
Update2: Thank you for all of your answers.
I would like to clarify the question as I did a bit of research on DAE representations and their applications in software.
There are 2 representations used ...
0
votes
0answers
49 views
3
votes
1answer
238 views
1
vote
1answer
65 views
Parametric plot of data from NDSolve
I have been trying to plot the solution of a set of differential equations solved used NDSolve. Now, in one of the cases, I have the find a parametric plot of the ...
5
votes
1answer
133 views
NDSolve::femcmsd: The spatial derivative order of the PDE may not exceed two
I was in the impression that V12 can now handle higher order PDES but for this particular case it fails to produce any solution.
...
0
votes
1answer
63 views
Plot a family of solutions of ODE with singularity
In the post Use Mathematica to plot the flow of an ODE with discontinuity, the following ODE with discontinuous coefficient was solved
...
0
votes
2answers
52 views
Delay in the beginning of solution for two ODEs
I have two couple ODEs and the second one has a delay in the time for starting. I mean, the first ODE starts at t=0 and the second one at t=20. How can I solve the second one in the correct time ...
2
votes
0answers
91 views
Model 1D Vlasov Equation
Vlasov Equation
The non-relativistic form of the Vlasov equation is given by:
$$
\partial_{t} f\left( \mathbf{x}, \mathbf{v}, t \right) + \mathbf{v} \cdot \nabla f\left( \mathbf{x}, \mathbf{v}, t \...
3
votes
1answer
85 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,...
0
votes
0answers
36 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 ...
0
votes
0answers
56 views
how to solve the integral diffenertial equation with convolution? [closed]
several days ago i have put up the question as this and links are as this
enter link description here
and i have simplify the question and
questions are as this
my question is as this and i want ...
6
votes
1answer
239 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. ...
1
vote
1answer
106 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
votes
0answers
63 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
votes
1answer
79 views
I can't get DSolve to work on coupled equations
In trying to solve a geodesic equation, I have these coupled equations:
...
-1
votes
0answers
44 views
3
votes
1answer
84 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)}{\...
0
votes
0answers
94 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 ...
0
votes
0answers
95 views
Determining the price of an option using Black-Scholes
Code for randomly generated interest rates:
...
7
votes
1answer
126 views
0
votes
1answer
128 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
votes
1answer
40 views
6
votes
1answer
307 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:
...
