Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
0
votes
0answers
37 views
Abridging Lists of Equations within NDSolve, Manipulate [duplicate]
I have a pretty little NDSolve function that I've finally decked out with manipulatable (by sliders) coefficients, which changes the graph in real time. However, I ...
-8
votes
0answers
81 views
Schrödinger equation in cylindrical coordinates [closed]
How can one numerically solve the nonlinear Schrödinger equation in cylindrical coordinates using Mathematica?
1
vote
0answers
75 views
Solar System Orbital Parameters [duplicate]
I recently made an n-body simulation and thought it would be interesting to try and model it on the interior of our solar system (Sun to Mars), but I cannot find initial conditions for such an ...
0
votes
0answers
41 views
Manipulate NDSolve with Constants [closed]
I am trying to solve this system of equations. I am running into an error that I cannot quite figure out. In this code, I use the constants ktotal and xtotal, where ktotal is the total amount of the ...
2
votes
1answer
70 views
Recursion depth exceeded
Below is my code for numerical solving of PDE with Crank Nicolson scheme.
...
1
vote
0answers
58 views
Indexing of Large System of Equations for Use in NDSolve
I currently have a list of ~150 DAE's (differential-algebraic equations) and I need to be able to work with using NDSolve. Fortunately I already have them ...
2
votes
2answers
87 views
4
votes
1answer
92 views
Solving an ODE in power series
How do I find a series solution to an ODE?
I do not mean taking the Taylor series of an exact solution; I want to solve nasty nonlinear differential equations locally via plug and chug. Surely, that ...
1
vote
0answers
65 views
What is wrong with this PDE?
I'm trying to get a numerical solution to the wave equation but Mathematica keeps on giving me an error and I cannot see what the problem is. This is the code I have:
...
0
votes
0answers
42 views
Strange Error in NDSolve [closed]
I am trying to numerically solve a long list of ordinary differential equations using NDSolve as follows:
...
3
votes
0answers
67 views
Using NDSolve for Integro-Differential Equations
I have a fairly complicated set of coupled non-linear integro-differential equations that I am trying to solve using NDSolve. The equations are:
...
1
vote
0answers
79 views
Performance in parameter estimation from ParametricNDSolve using varied initial conditions
I have 250 data points from a timecourse exeriment in a list, with columns specifying (1) time, (2-4) initial conditions, (5) absorbance reading. I want to fit 4 parameters (k1, k2, k3, k4) in a DAE ...
2
votes
1answer
57 views
NDSolve with vector function
(Possible duplicate yet I still can't understand.)
Basic 2D revolving around origin:
...
3
votes
1answer
145 views
White noise $\eta(t)$
How to make a random function $\eta(t)$ to insert in a differential equation for NDSolve?
Edit: example: to solve equations like $\frac{dx}{dt}=\eta(t)$
6
votes
2answers
174 views
How to deal with zero in NDSolve in mathematica?
I would like to solve the following ODEs
$$\begin{cases} x'(t)&=y\\
y'(t)&=-y(t)/t-e^{x(t)},\\
x(0)&=1,\\y(0)&=0,
\end{cases}$$
(EDIT :
The second equation used to be $y'(t) = ...
24
votes
2answers
414 views
Variable naming changes everything
I am having a rather unusual problem I do not understand with Mathematica where renaming one of the variables of my function causes the function to stop "working". Here is the example of the code ...
1
vote
0answers
91 views
NDSolve diffusion equation over/underdetermined
I have a feeling the solution to my problem is very simple… but my knowledge of differential equations is pretty weak.
I am trying to solve a scalar diffusion equation (used in NMR spectroscopy, but ...
0
votes
1answer
131 views
DAE - varying initial conditions
I want to solve a DAE-system and I want to vary more than one initial conditions and to manipulate them. I looked here:
Putting NDSolve into ParametricPlot
But it does not work:
...
16
votes
2answers
377 views
3D orbits and inaccuracy over time
I wrote a little program to use Newton's Law of Universal Gravitation to animate 3 planets orbiting a central star, but I have run into a problem. Here is the code that I used to create the program (I ...
2
votes
2answers
85 views
Mass Symbolic Manipulation with Subscripts? (from plaintext Input)
The simplest example of the change being sought is a greek letter, typed in as plaintext nu, and its may be replaced by the symbol, ν:
expr = 3nu*kx*ky+ ...
1
vote
1answer
89 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
140 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
50 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
63 views
2
votes
2answers
102 views
ODE and BVP: NDSolve errors
The mathematical problem is shown here. I tried to solve writing the
...
1
vote
1answer
139 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
77 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
94 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
190 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
64 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
70 views
1
vote
0answers
113 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 ...
0
votes
0answers
72 views
How can I solve differential equation of the Bass diffusion model? [closed]
This is my first posted question.
I want to do some research about applying the Bass diffusion model to software reliability.
I tried to derive this model step by step. When I tried to solve Bass' ...
2
votes
1answer
69 views
Infinite Expression Error from NDSolve
I am trying to solve a differential equation numerically. So I have
...
3
votes
3answers
145 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
59 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
95 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 ...
7
votes
2answers
290 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 $\dot x = y$ , $\dot y = -9\sin(x) - 0.20y$ and have gotten nowhere.
4
votes
1answer
165 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
62 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
96 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
98 views
Distance between two functions satisfying a constraint
My problem is that I have two functions that are described as follows:
...
2
votes
0answers
74 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 ...
1
vote
1answer
96 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
165 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
125 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
99 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
82 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
76 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
51 views
DSolve::overdet for system of linear PDEs
I would like to resolve symbolically the following equation:
...
