Tagged Questions

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

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-3
votes
1answer
189 views

NDSolve doesn't solve my system of ODEs

What is causing the error in this code? ...
0
votes
2answers
251 views

Autonomous equations' critical points and eigenvalues

I have three-dimensional autonomous equations and want to find their critical points and corresponding eigenvalues. They have 6 critical points each. x, ...
0
votes
0answers
173 views

How can I solve my non-linear ODE?

DSolve[{-x^2 + y[x]^2 - 2 x*y[x]*y'[x] + 2*x^2 *y'[x]^2 == a^2}, y[x], x] DSolve is returning the input statement unevaluated. ...
3
votes
1answer
254 views

How can I deal with a non-numerical value for a derivative at $t = 0$ when using NDSolve?

I want to solve two coupled equations with NDSolve, ...
17
votes
2answers
2k views

How to fit 3 data sets to a model of 4 differential equations?

I'm a biologist and a newbie in Mathematica. I want to fit three data sets to a model consisting of four differential equations and 10 parameters. I want to find the parameters best fitting to my ...
8
votes
1answer
385 views

Complex valued 2+1D nonlinear PDE using NDSolve

I am trying to follow the main ideas presented in this question, applying it to my own problem, which is a complex, time-dependent, nonlinear PDE: $$i \frac{\partial \psi}{\partial t} = \left[ ...
6
votes
1answer
243 views

solve ODE with divergencies

The solutions of the second order differential equation $$\frac{1}{\eta}\frac{d}{d\eta}\left(\eta \frac{df}{d\eta}\right)+\left(1-\frac{s^2}{\eta^2}\right)f-f^3=0$$ is shown in Fig. 5.2 below, for ...
2
votes
0answers
62 views

Are FEM methods integrated in NDSolve yet? [duplicate]

About a year ago there was a discussion on these forums as to whether FEM methods have already been integrated into NDSolve in Mathematica. The answer back then was ...
4
votes
0answers
776 views

Numerically solving system of partial differential equation

I am trying to solve a system of partial differential equation with boundary conditions. But I got an error message saying NDSolve::icfail: Unable to find initial ...
5
votes
1answer
152 views

Set some Method options for NDSolve globally while allowing others to change

In a code base that is difficult to change for unrelated issues, I have many invocations of NDSolve that look like the following: ...
3
votes
1answer
428 views

How to increase Maximum number of steps in any other functions except NDSolve?

I want to plot an output response from a state space model. I use StateResponse[] to calculate it and then plot it. When I run my code, I face this message: ...
22
votes
2answers
1k views

Complex valued 2+1D PDE Schroedinger equation, numerical method for `NDSolve`?

Based on the heat equation of the Mathematica Manual tutorial, I wrote the complex counterpart (Schroedinger) equation, for the free particle propagation of an initial wavepacket. ...
1
vote
4answers
270 views

Calculating difference ratios (Δβ/Δρ) from a data set

I am little bit confused about how to calculate δβ/δρ value if I have set of values like this. I have the values of β and ρ like this. ...
16
votes
2answers
2k views

Elegant way of obtaining the envelope of oscillating function [duplicate]

I am solving a differential equation numerically and the output is an oscillating function with the amplitude of the oscillation decaying in time. I would like to extract the power law governing this ...
4
votes
1answer
602 views

Solve inhomogeneous Poisson's equation, gives no result at all

I would like to solve the following two-dimensional inhomogeneous Poisson's equation in Mathematica including specific boundary conditions, and I know that an analytical solution exists, but ...
6
votes
1answer
206 views

Specifying mesh in NDSolve

I am trying to solve a system of one-dimensional two-point boundary-value problems with NDSolve. I would like use a fixed mesh (specified by me) in the calculation. Is there a way to do this? The ...
0
votes
0answers
228 views

DSolve expression doesn't evaluate

Can Mathematica solve $\; d^2/dx^2{}+ (1/x) d/dx\;$ form of equations? For example, I am trying to solve the system of equations given below: ...
1
vote
1answer
339 views

BVP - shooting method

I really don't know how to realize this method. The examples in internet and the reference aren't helpful for me. 1) I have the values for today: ...
1
vote
0answers
239 views

Why is a bump function making NDSolve take forever to solve?

I am attempting to solve a system of relatively complicated elliptic PDEs via a relaxation technique. In particular, I am trying to solve $\textrm{div} LW = S$ where $S$ is some vector and $L$ is the ...
-7
votes
4answers
445 views
2
votes
1answer
194 views

boundary problem

I have some conditions at t=0, like r1^2+r2^2=0.5 and x^2+y^2=6 and I want to find the right ...
1
vote
1answer
108 views

Using Dot Product with InterpolatingFunctions

I am using NDSolve on a vector function $\mathbf y'(x)=f[\mathbf y(x)]$ with initial condition $\mathbf y_0$, where the dimension of the vector should be user-defined. ...
4
votes
1answer
205 views

My mistake or error in NDSolve?

I try to solve the following equation $$y'=y-2ye^{-0.8y}, \quad y(0)=0.7.$$ By some aruments I expect to have a positive solution $y(t)\geq0$, for all $t>0$, however, NDSolve shows that starting ...
1
vote
0answers
268 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
votes
1answer
561 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
votes
1answer
205 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
1answer
538 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
737 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
votes
1answer
185 views

Unresolved differential equation [closed]

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

Non-Solvable PDE?

I would like to know whether this PDE is solvable and if yes, for which values of $a$. ...
0
votes
0answers
123 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
431 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
363 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
votes
1answer
249 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 ...
3
votes
1answer
528 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 ...
1
vote
1answer
392 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
209 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
606 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
807 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 ...
5
votes
0answers
120 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
274 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
vote
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
424 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
456 views

Recursion depth exceeded

Below is my code for numerical solving of PDE with Crank Nicolson scheme. ...
3
votes
1answer
202 views

Indexing of Large Autonomous System of Equations for Use in NDSolve

I currently have a list of ~150 autonomous ODE's that I need to be able to work with using NDSolve. Fortunately I already have them formatted in plaintext, which ...
2
votes
2answers
317 views

Strange Behavior of NDSolve

I am trying to evaluate the following ODE numerically: ...
11
votes
2answers
2k 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
618 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
288 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 ...