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
894 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
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0answers
122 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
295 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
489 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
544 views

Recursion depth exceeded

Below is my code for numerical solving of PDE with Crank Nicolson scheme. ...
3
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1answer
204 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
328 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
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0answers
706 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
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0answers
301 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
407 views

NDSolve with vector function

(Possible duplicate yet I still can't understand.) Basic 2D revolving around origin: ...
3
votes
1answer
748 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
751 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
1k 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
452 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
240 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: ...
19
votes
2answers
941 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
398 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
431 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. ...
8
votes
0answers
463 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
133 views
3
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2answers
986 views

ODE and BVP: NDSolve errors

The mathematical problem is shown here. I tried to solve writing the ...
3
votes
1answer
930 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
466 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 ...
3
votes
3answers
732 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
140 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
549 views
1
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0answers
277 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
455 views

Infinite Expression Error from NDSolve

I am trying to solve a differential equation numerically. So I have ...
3
votes
3answers
287 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
256 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
334 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 ...
13
votes
2answers
1k 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
584 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: ...
3
votes
1answer
211 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 ...
0
votes
2answers
459 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
193 views

Distance between two functions satisfying a constraint

My problem is that I have two functions that are described as follows: ...
4
votes
1answer
299 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
285 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
376 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, ...
3
votes
2answers
422 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
192 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
2answers
944 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
218 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 ...
0
votes
0answers
290 views

DSolve::overdet for system of linear PDEs

I would like to resolve symbolically the following equation: ...
0
votes
2answers
294 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 ...
17
votes
1answer
1k 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
220 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
93 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 ...