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

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1
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0answers
223 views

Change of coordinates for an InterpolatingFunction

This is a toy example of the question I have but I think it illustrates the point. I have a function y[x] which is an interpolating function. Let's define it ...
2
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1answer
450 views

How to take the derivative w.r.t. an arbitrary function?

EDIT: The answer posted by @Jens works for built-in functions only. However I'm starting to wonder if this is related to my Mathematica install somehow. I have version 7. Here is an example in the ...
5
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1answer
190 views

VariationalD giving the wrong solution?

EDIT: As pointed out in the comments, VariationalD gives a variational derivative (which I don't want), not a derivative with respect to a function (i.e. ...
0
votes
0answers
419 views

Solving coupled eigenvalue differential equations

I am trying to solve an equation of the form as follows $\left(\begin{array}{cc} -\frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}+\sin^{2}\left(z\right) & z\\ z & ...
4
votes
2answers
664 views

Does Mathematica have a command analogous to ode45 of MATLAB?

Does anybody know if Mathematica has an analogue of MATLAB's ode45 command? I need to solve a second order coupled ODE system of equations.
2
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1answer
174 views

Unresolved differential equation [closed]

Why can't Mathematica solve this equation as stated? ...
0
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0answers
98 views

Non-Solvable PDE?

I would like to know whether this PDE is solvable and if yes, for which values of $a$. ...
0
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0answers
116 views

Integrating and plotting pde system solution

I have a trouble with plotting a pde system solution. I'm solving a PDE system in 2-dimensional space and then I want to integrate the solution along one dimension and build a log plot along the ...
5
votes
2answers
405 views

How to graph a series of coupled oscillators and watch the wave move along them

Here are the differential equations that set's up the 11 coupled oscillators. ...
0
votes
1answer
330 views

Parametric Plot of coupled differential equations

I am able to plot a graph of all the differential equations, but I'd like a parametric plot of each individual one. Here is what I have so far. ...
9
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1answer
226 views

WhenEvent and partial derivatives

Can WhenEvent be used to reset the conditions on a PDE at a given time? How would the syntax of that be? This is the code I`m using ...
6
votes
2answers
1k views

Finding y given x from an interpolating function

I would like to put a dot on the point of a curve that has a specific y value but I don't know the x value. A simple example of my code is ...
2
votes
1answer
448 views

Monitoring the Evaluation of NDSolve: time to finish estimation

My problem is quite simple: I run a NDSolve with a system of many ODEs, a calculation that will run for many hours, and I would like to know the progress of the ...
0
votes
1answer
81 views

Weird output when solving this differential equation [closed]

I encountered this weird output when solving this differential equation. The problem: Solve y' + y tan(x) = sin(2 x) given y=2 when x=0 and verify the solution. My code: ...
1
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1answer
343 views

Solving differential equations with constraints

The problem is $$ x''(t)=F(t) - kx'(t) \\ x'(0)=x(0)=0$$ with the additional constraints $$ 0 < x(t) <a \\ 0 < x'(t) <b $$ where $F(t)$ is a known function and $a,b,k$ are given. At the ...
1
vote
1answer
165 views

system of ODE through NDSolve

I am quite puzzled to solve the coupled ode's numerically. Please tell me why it runs for a long time and not giving any output in mathematica. I am using NDsolve. please have a look ...
1
vote
1answer
520 views

Integro-differential eqn with double integral

I am looking at the following variation of a integro-differential, with y[0]=1. The output is not great, any solutions to this? ...
1
vote
0answers
672 views

NDSolve: methods and step size choosing

I am looking into the documentation of NDSolve[]; more precisely how this function chooses the StepSize and how it chooses which ...
4
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0answers
116 views

Numerical solution of Schrödinger-type equation in Mathematica [duplicate]

I want to solve the following differential equation numerically: \begin{equation} i\partial_{t}\psi(r,t)=\left[-\frac{\Delta}{2m}+g\left|\psi(r,t)\right|^{2}+V_{d}(r,t)\right]\psi(r,t) \end{equation} ...
0
votes
2answers
251 views

Plotting geodesics of upper half plane

I want to solve (numerically) the geodesics of the upper half plane and plot. The results are quite known (i) straight lines parallel to $y$-axis and (ii) semicircles centered on the $x$-axis. Now the ...
1
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0answers
60 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 ...
1
vote
0answers
381 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 ...
2
votes
1answer
355 views

Recursion depth exceeded

Below is my code for numerical solving of PDE with Crank Nicolson scheme. ...
2
votes
1answer
145 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 ...
2
votes
2answers
272 views

Strange Behavior of NDSolve

I am trying to evaluate the following ODE numerically: ...
8
votes
1answer
1k 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 ...
3
votes
0answers
507 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: ...
0
votes
0answers
258 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
321 views

NDSolve with vector function

(Possible duplicate yet I still can't understand.) Basic 2D revolving around origin: ...
3
votes
1answer
565 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 $\frac{dx}{dt}=\eta(t)$
5
votes
2answers
639 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) = ...
31
votes
2answers
902 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
1answer
372 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
211 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: ...
18
votes
2answers
777 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
340 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+ ...
2
votes
1answer
340 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. ...
6
votes
0answers
384 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 ...
5
votes
1answer
119 views
3
votes
2answers
771 views

ODE and BVP: NDSolve errors

The mathematical problem is shown here. I tried to solve writing the ...
3
votes
1answer
698 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
345 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 ...
2
votes
3answers
645 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
127 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
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2answers
415 views
1
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0answers
248 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
387 views

Infinite Expression Error from NDSolve

I am trying to solve a differential equation numerically. So I have ...
3
votes
3answers
265 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 ...
2
votes
1answer
194 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 ...
2
votes
4answers
286 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 ...