Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
2
votes
0answers
21 views
Increasing NDSolve time step size
I recently tried creating a solar system simulation using the "n-body problem" formulation and NDSolve, but have run into a little problem. I've managed to get accurate initial positions and ...
2
votes
1answer
74 views
Indexing of Large Autonomous System of Equations for Use in NDSolve
I currently have a list of ~150 autonomous DAE's (differential-algebraic equations) that I need to be able to work with using NDSolve. Fortunately I already have ...
1
vote
1answer
105 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
0answers
47 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
84 views
Schrödinger equation in cylindrical coordinates [closed]
How can one numerically solve the nonlinear Schrödinger equation in cylindrical coordinates using Mathematica?
1
vote
0answers
85 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
43 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 ...
1
vote
1answer
68 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 ...
0
votes
1answer
340 views
How can I understand the result Mathematica returns from DSolve?
I have solved an ODE using DSolve, but I have a problem with understanding the solution.
In general the solution is in the form:
...
2
votes
1answer
71 views
Recursion depth exceeded
Below is my code for numerical solving of PDE with Crank Nicolson scheme.
...
0
votes
1answer
84 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
...
2
votes
2answers
87 views
4
votes
1answer
96 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 ...
4
votes
1answer
244 views
Can DSolve solve systems with unspecified function coefficients?
I am an economic research student with no previous experience with Mathematica, so please pardon me if my questions sounds really stupid.
I am hoping to solve a system of nonlinear ODEs symbolically. ...
1
vote
0answers
66 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:
...
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 ...
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:
...
2
votes
1answer
60 views
NDSolve with vector function
(Possible duplicate yet I still can't understand.)
Basic 2D revolving around origin:
...
3
votes
0answers
69 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:
...
6
votes
2answers
179 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) = ...
3
votes
1answer
147 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 $\frac{dx}{dt}=\eta(t)$
0
votes
1answer
137 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:
...
24
votes
2answers
419 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 ...
16
votes
2answers
385 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
88 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
142 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 ...
6
votes
1answer
63 views
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 ...
3
votes
1answer
167 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:
...
2
votes
2answers
102 views
ODE and BVP: NDSolve errors
The mathematical problem is shown here. I tried to solve writing the
...
2
votes
1answer
126 views
Is it possible to impose “Assumptions” in DSolve or equivalent? (differential equation solving)
When DSolve tries to solve differential equations, it is sometimes not smart enough to generate conditions according to different possible value of parameters. ...
3
votes
2answers
193 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) = ...
2
votes
1answer
142 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
95 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. $\lambda(x)$), ...
1
vote
0answers
114 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 ...
8
votes
1answer
344 views
1D Euler Equations
Is it possible to accurately solve the 1D Euler equations in Mathematica using NDSolve?
For example, let us consider the problem given here: http://www.csun.edu/~jb715473/examples/euler1d.htm
Using ...
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:
...
4
votes
1answer
383 views
Solve system of ordinary differential equations that doesn't have an initial condition (t=0), but has an inifinity condition (t=infinity)?
I have a question for solving t -> Infinity on Mathematica. First, I have a system of ODEs:
...
0
votes
1answer
74 views
0
votes
0answers
73 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
1answer
246 views
Eliminating functions from system of PDE in Mathematica
Mathematica users,
Let's see an example of three PDEs:
How can I eliminate variables q1[x,y,z] and q2[x,y,z] from a system of ...
1
vote
1answer
180 views
Finding numerical/analytic solution to a derivative
Consider the following system of equations, with 11 dependent variables:
...
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
4answers
98 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 ...
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 ...
7
votes
2answers
295 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.
0
votes
1answer
277 views
Steady states and eigenvalues for a non-linear system:
I am trying to understand a non-linear system of equations, and find their steady states and dynamics. I am noob to understanding Mathematica (I am using version 6, but I have access to the latest ...
