Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
1
vote
1answer
105 views
How to adjust parameters to experimental data on a NDSolve problem
I have 2 differential equations with 2 variables, x and y,which are a function of t and I have the parameters k1, k2 y k3.
...
7
votes
0answers
163 views
Numerically solve 2nd order differential equation with singularity
Consider a second order differential equation with a potential that diverges at some generic value in the variable. For example:
$$-y^{\prime\prime}(s)+\frac1{\mathrm{cn}{(s\mid k^2)}}y(s)=0$$
where ...
0
votes
0answers
55 views
DSolve isn't working right [closed]
So, I went to wolfram's page here: http://reference.wolfram.com/mathematica/ref/DSolve.html
I took a DSolve example and copy-pased it into my own mathematica notebook, but I got a vastly different ...
6
votes
1answer
68 views
2
votes
2answers
122 views
ODE and BVP: NDSolve errors
The mathematical problem is shown here. I tried to solve writing the
...
3
votes
1answer
206 views
How to plot and solve the numerical solution of a integro-differential equation
I have a integro-differential equation of the form
$y'(t) = - \int_0^t {y(t_1 )} e^{t_1 - t} dt_1, {\rm{ t}} \in {\rm{[0,10], y(0) = 1}}$
My code is:
...
1
vote
1answer
86 views
What does the Error Message in DSolve really mean?
Having this ordinary non linear differential equation
$$y'-x^2 (y+1)\cdot (y+2)^2= 0$$
with the boundary condition $y(4)=2$. When trying to solve this one with Mathematica by using
...
0
votes
0answers
111 views
ode with boundary value problem does not work [closed]
I have to solve the following boundary value problem:
$$
\varphi'(\lambda) + \beta(\lambda) \lambda_x^2 +\gamma(\lambda)\lambda_{xx} = k
$$
where $\lambda$ is a function of $x$ (i.e. $\lambda(x)$), ...
3
votes
2answers
220 views
Plotting heat equation in a Manipulate expression
I have a 2D heat equation $u_t = \alpha (u_{xx} + u_{yy})$ with conditions:
$u(x, y, 0) = 300$,
$u_y(x, 0, t) = \mu_1(x)$,
$u_y(x, 1, t) = \mu_2(x)$,
$u(0, y, t) = \mu_3(y)$,
$u(1, y, t) = ...
0
votes
1answer
68 views
Notation for numerical solutions to differential equations
Can somebody explain this notation to me? Using Mathematica's first example in the NDSolve documentation:
...
0
votes
1answer
86 views
1
vote
0answers
132 views
Adapting NDSolve to circumvent NDSolve::bdord: error for 1-D Euler Equations
I attempted to use NDSolve for the 1-D isentropic unsteady flow equations with low subsonic inflow velocity and prescribed inflow total enthalpy; along with a ...
2
votes
1answer
85 views
Infinite Expression Error from NDSolve
I am trying to solve a differential equation numerically. So I have
...
3
votes
3answers
157 views
Mathematica not able to confirm its own solution to differential equation
I type the following into Mathematica:
DSolve[q''[x] + 2 x/(x^2 - 1) q'[x] - 4*q[x]/(x^2 - 1) == 0, q[x], x]
It gives me the result
...
3
votes
1answer
67 views
How to integrate ParametricNDSolve solution with respect to a parameter?
I have just upgraded to the new version of Mathematica because of its new built-in ParametricNDSolve function. I need to solve a first-order non-linear ordinary ...
3
votes
4answers
114 views
Problem with WhenEvent
I am trying to add a time dependent fraction to a parameter in NDSolve,
i.e. when 10 < t< 20, add ...
8
votes
2answers
357 views
Basins of Attraction
How does one shade the basin(s) of attraction of a phase plot in Mathematica? I have been trying to do this using the system
$$\begin{align*}
\dot x &= y\\
\dot y &= -9\sin(x) - 0.20y
...
3
votes
1answer
199 views
NDSolve for a large system of simple ODEs
I am solving a system of many (more than 100) ODEs.
It is the kind of standard rate equation encountered in semiconductor physics.
Here is the system:
...
4
votes
1answer
74 views
Differentiating ParametricNDSolve solutions
Is there any way to differentiate a solution obtained by ParametricNDSolve? For instance, I have the position $\phi_\gamma(t)$ as a function of time, parametrized ...
1
vote
2answers
109 views
NDSolve solution for driven damped pendulum diverges
I want to solve numerically for the system of the driven damped pendulum using Mathematica. This is the second-order nonlinear equation
\begin{equation}
\ddot{x} + 2 \beta \dot{x}+ \omega_0^2 \sin
...
3
votes
1answer
106 views
Distance between two functions satisfying a constraint
My problem is that I have two functions that are described as follows:
...
3
votes
1answer
84 views
Using a user defined NormFunction in FindFit or NDSolve
I would like to use a different norm instead of the 2-norm in FindFit (Mathematica 9). For example, instead of using
$$\sqrt{\sum (x_{\mathrm{model}} - ...
2
votes
0answers
82 views
Conditional statements in intial conditions?
This is potentially a daft question, but I thought I'd ask it; I have some material free to diffuse in a boundary between rn and ro; I've been able to get it working nicely for neumann type boundary ...
2
votes
1answer
107 views
Non linear equation phase space
As a supplementary to my question solution of differential equation I post a new question of how is it possible to make a Table that has elements the solutions of a non linear differential equation, ...
2
votes
2answers
182 views
Animating the Lorenz Equations
I am trying to use the Animate command to vary a parameter of the Lorenz Equations in 3-D phase space and I'm not having much luck.
The equations are:
...
0
votes
1answer
132 views
solution of differential equation
I have the following code that gives you a phase portrait of a 2d system and I can't understand what means the 3rd and 4th line (sol1 and sol2).
...
1
vote
1answer
106 views
How does one specify Neumann conditions for NDSolve?
I have a series of functions defined in my notebook, and then want to use this to solve a diffusion-reaction type equation. At the moment, something like this works:
...
4
votes
2answers
94 views
Problem with adding vector to symbolic function (for NDSolve)
I'm trying to set up a system of differential equations for passing to NDSolve. Note that my initial conditions are vector valued so Mathematica should know that ...
-3
votes
2answers
88 views
Problem with simple DSolve [closed]
This is my code:
ode = x'[t] == (x[t] (x[t] + 1))/(t (t + 1));
sol = DSolve[ode, x[t], t] // Simplify
Then I get this output for sol:
$$\left\{\left\{x(t)\to ...
0
votes
0answers
53 views
DSolve::overdet for system of linear PDEs
I would like to resolve symbolically the following equation:
...
1
vote
1answer
145 views
Problems with NDSolve and stiffness
I am trying to solve an ODE in chemical kinetics:
$$\begin{align*}
\frac{\mathrm d[x]}{\mathrm dt} &= -k_1 [x][y]\\
\frac{\mathrm d[y]}{\mathrm dt} &= k_1 [x][y] - k_3[y]
\end{align*}$$
My ...
13
votes
1answer
312 views
Optimizing a Numerical Laplace Equation Solver
Laplace's Equation is an equation on a scalar in which, given the value of the scalar on the boundaries (the boundary conditions), one can determine the value of the scalar at any point in the region ...
2
votes
1answer
113 views
Plot differential equation system in a complex way
Based on this differential equation system:
$$\begin{align*}
\dot{x}&=f(x,y)\\
\dot{y}&=g(x,y)
\end{align*}$$
where
$$\begin{align*}
f(x, y)&=x^2+y^2-25\\
g(x, y)&=x^2-y^2-7
...
1
vote
1answer
70 views
Using Manipulate Feature for Two ODE's
So I have not been able to find any examples of the Manipulate feature for two ODE's. I would like to plot a graph of x[t] vs. y[t] and manipulate the initial conditions, v and theta. Thank you very ...
3
votes
1answer
62 views
How could I find the singular solutions of an ODE?
Starting with the equation
$$y^{\prime\prime}x^2={y^\prime}^2$$
I could only get the general solution using DSolve:
...
1
vote
2answers
495 views
Solving a system of ODEs with the Runge-Kutta method
I´m trying to solve a system of ODEs using a fourth-order Runge-Kutta method. I have to recreate certain results to obtain my degree. But I'm a beginner at Mathematica programming and with the ...
3
votes
2answers
146 views
How to remove a singularity with WhenEvent
Bellow I have a differential equation which hits a singularity at low values of t. What I want to do is somehow utilize the WhenEvent command in order to replace ...
0
votes
2answers
66 views
characteristic polynomial based on differential equation
I have this differential equation:
$$\ddot{x}-\frac{1}{6} \dot{x} - \frac{1}{6}x = e^t$$
When I DSolve it looks like this:
...
0
votes
1answer
98 views
NDSolve complains about missing derivatives of dependent variables in Mathematica 9
In Mathematica 8
NDSolve[{x[t] == 1, x[0] == 1}, x[t], {t, 0, 10}]
solves fine and returns
...
0
votes
1answer
104 views
1
vote
2answers
141 views
Solve Differential equation system
I've tried to solve this differential equation system, buy without any luck.
This is my code:
...
1
vote
2answers
137 views
How can I use FindRoot on an expression from NDSolve?
I have a second order ODE that I can only solve numerically using NDSolve, but I then need to use the solution in FindRoot and am running into errors. A simplified but analogous problem is the ...
0
votes
0answers
89 views
NDSolve divergence in Mathematica 9
I have been working with Mathematica 7 and 8 to numerically solve partial differential equations by MethodOfLines of NDSolve. ...
3
votes
1answer
179 views
Create Euler equation
I've tried to make some research, but without any luck.
How do I setup the Euler equation for this in Mathematica?:
$ \text{Min} \int_0^1\left(2x^2+ \left(4t-5 e^{r \, t} \right) x \, \dot{x} + ...
4
votes
2answers
138 views
3
votes
1answer
201 views
Tutorial for basic numerical methods for PDEs
I'm afraid this is probably not going to be a "good" question, but I'd like to use Mathematica to learn about basic numerical schemes for solving pdes. For example, I'd like to compute the solution of ...
3
votes
2answers
122 views
Putting NDSolve into ParametricPlot
I am having issues using Manipulate to plot the (numeric) solution to an ODE for different parameter values.
I have a code that has several stages, which seem to ...
6
votes
0answers
64 views
Modify NDSolve`StateData (if possible)
I am trying to solve a PDE that needs to be scaled constantly (refer to this). @andre suggests I modify NDSolve`StateData.
Now, the problem is, I'm not used to ...
2
votes
2answers
277 views
NDSolve: Normalizing at every step
Suppose I have an transport equation with an initial conditions:
...
2
votes
2answers
118 views
BC for transport equation using NDSolve
First I can solve a transport equation with a source (Is it still called transport equation?) using DSolve. The form of the source serves only as an example. It can ...
