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

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6
votes
1answer
98 views

code is ignoring WhenEvent

I would like the value of x[t] to be equal to 0 when it has a negative value so I used WhenEvent but it has no effect on my code ...
0
votes
0answers
42 views

Is there a way to pre-calculate a slow animation and then run easily with no lag? [duplicate]

I have an animation of a triple pendulum on a moving base, however even after trying to change the whole coding to make it faster by using module and all it is still pretty bad as I need it to be ...
-2
votes
2answers
81 views

Error in the solving of the simultaneous Ordinary Differential Equation [closed]

As I am trying to get the solution of the simultaneous ordinary differential equations ...
4
votes
2answers
200 views

DSolve misses a solution of a differential equation

[Note that in the cited duplicate, DSolve not finding solution I expected, the general solution returned by DSolve is missing a solution for quite different reasons ...
5
votes
0answers
82 views

DSolve returns an answer that is not a solution

Investigating DSolve misses a solution of a differential equation, I came across this odd behavior of DSolve. The following DSolve command returns an answer to the ...
2
votes
2answers
90 views
5
votes
3answers
303 views

Implementing Picard's Iteration for solving ODEs

Picard's Iteration is a way of solving the IVP $$y'(x)=f(x,y(x)), \quad y(x_0)=y_0 $$ It consists of defining the following sequence of functions recursively: $$y_0(x):=y_0 \\ ...
4
votes
0answers
70 views

Extraneous reaped data with NDSolve and WhenEvent

Bug introduced in 9.0 or earlier and fixed in 10.1 In exploring What is the range of values $x$ for which $f(x)$ is higher than $k$ over a given domain?, I came across the following strange ...
2
votes
0answers
287 views

Crank-Nicolson scheme for the Schrödinger equation

I am trying to solve the 1-D Schrödinger equation with the Crank-Nicholson method. I use the atomic units: time < 10^-14 => 413 a.u.t. length 30 * 10^-9 m => 567 Bohr radii ...
0
votes
1answer
143 views

How to solve constraint differential equations using If function

I have to solve a series of differential equations along with a constraint that has to be satisfied at each point of time where $t\in [0, 100]$ The model parameters are ...
2
votes
1answer
88 views

Potential flow over cylinder with FEM: Pressure field is flipped

Much in the fashion of a few problems already answered on Mathematica.SE (1, 2), I am trying to solve the Laplace equation in velocity potential $\phi$ to simulate irrotational, inviscid flow over a ...
-5
votes
1answer
64 views

how to change parameters in NDSolve? [closed]

I want to solve a PDE with parameters chosen based on the sign of derivative. For instance in the following PDE ...
2
votes
1answer
116 views

How can I write a loop to get many values from a solution?

I am looking at the value of x[t] at day t = 200 over several years. I tried to do it using a For-loop but it didn't work. This ...
0
votes
0answers
68 views

PDE: Inconsistent equation dimensions

EDIT: I need to solve the following PDE: $\nabla^2\vec{A}=-\mu_{0}\vec{j}$ where $\vec{j}=\sigma\vec{E}$ and $\sigma=1*10^{10}$ which basically boils down to three different PDE's; ...
3
votes
2answers
79 views

Error control for NDSolve

I have a problem controlling the numerical error associated with the following non-linear ODE : ...
11
votes
1answer
208 views

How to specify PDE Boundary condition on Bspline?

Context I would like to solve a PDE on a boundary which is parametrized as a BSpline. I am trying to solve the force-free Grad-Shafranov equation on a ...
0
votes
1answer
51 views

Output with NDSolve

I use of the following differential equation: s = NDSolve[{y'[x] == y[x] Cos[x + y[x]], y[0] == 1}, y, {x, 0, 30}] Output. The solution in a plot. What is ...
2
votes
1answer
240 views

Runge-Kutta-2 on System

After spending some time using the Mathematica documentation and this Mathematica.SE answer, I implemented the Runge-Kutta-2 routines. I am hoping someone can validate what I did and tell me that it ...
4
votes
1answer
133 views

Unexpected results from trying to solve Laplace's equation

I am trying to find the solution to Laplace's equation: $\dfrac{\partial^2 u}{\partial x^2}+\dfrac{\partial^2 u}{\partial y^2}=0$ over the following region of space: the vertices of the triangle ...
0
votes
0answers
62 views

Two warning messages in NIntegrate and NDSolve

Everybody I am trying to replicate the Figure.7 of the article arXiv:1103.2683 However my plot is different from it, which is as follows Then we can find the differences between both figures, first ...
0
votes
1answer
89 views

How to resolve the singularity in NDSolve

I ran into a problem in my Mathematica code. There is a singularity or stiff system in NDSolve. The explicit code is as follows: ...
7
votes
1answer
566 views

How to solve fluid flow problem based on Navier-Stokes equations?

Does anyone know or can provide any examples how fluid flow problem can be formulated and solved in Wolfram Language? Simplest cases of 1D or 2D flows based on Navier-Stokes equations or even their ...
1
vote
2answers
65 views

NDSolve giving NDSolve::deqn: message when given my system of equations [closed]

I am so new on Mathematica. I hope my question is suitable. I have looked the Documentation Center and looked also on StackExchange but I could not handle the problem. It gives always the error ...
2
votes
3answers
356 views

How can I apply calculus to functions obtained from NDSolve?

Originally, I asked the question below, but the real underlying issue is as follows: When we solve an ODE numerically, I get the answer like this: ...
0
votes
0answers
39 views

How do I solve first order non-linear system of PDE: $\partial f^i(x,y)/\partial z = F^i(f^1,f^2,…,f^n)$?

I've previously posted this question in Mathmatics.SE but never receive a response. The old post can be found here: ...
1
vote
0answers
100 views

How can I solve the 2D Laplace equation with Neumann boundary conditions? [closed]

I would like to solve the following boundary value problem for $u(x,y)$: PDE $\quad \quad \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0$ Domain $\quad \quad 0 \le x \le ...
11
votes
1answer
413 views

Inconsistent results of second derivative of inverse fourier transform

Bug introduced in 9.0 or earlier and persisting through 10.2.0 I am trying to get the Green's function of a toy diffusion equation $$\frac{\partial^2 u(x,t)}{\partial x^2} = ...
0
votes
1answer
68 views

Solving an NODE in series

How can I solve this NODE in series y''[x]^2 + (1/2)*y'[x] + (1/2) y[x] == p x + q. `p` and `q` are constant. But do not know how to actually solve it with ...
0
votes
0answers
68 views

Solving a series of non-homogeneous differential equations

I have the following system of differential equations $$\rho1(t) = {(c1-\lambda(t))\over 2k1} $$ $$\dot\lambda(t)={\beta \lambda(t)-{(c1-\lambda(t))^2\over 4k1}}$$ and $$\rho2(t) = {(c2-x(t))\over ...
-1
votes
1answer
64 views

ParametricPlot not plotting the results I'm getting from NDSolve

I try to plot a phase diagram with ParametricPlot but everytime Mathematica does nothing. I start by ; ...
1
vote
0answers
88 views

How to obtain the magnetic field of the following set up [closed]

This is the experimental set up: A ferromagnetic cylindrical disk (of irrelevant dimensions) has either sides set at different electric potentials (left side at 0 volts and right side at 1 volt). A ...
1
vote
1answer
79 views

If[ ] not evaluating properly inside NDSolve[ ]

I am trying to solve a set of equations with the NDSolve. I encounter an error which I try to explain it with the below example. ...
4
votes
1answer
67 views

NDSolve returns asymmetric solution to a symmetric equation

I am trying to find the potential of a conducting cylindrical electrode by solving the Laplace's equation. Both, the boundary conditions and the equation are symmetric w.r.t. the change $r\to-r$. ...
32
votes
2answers
1k views

Variable naming changes everything

Bug fixed in 10.0.0 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 ...
6
votes
1answer
109 views

Accuracy of Grad-Shafranov PDE's NDSolveValue over implicit region

Context I need to solve for the toroidal flux of the magnetic field above an accretion disc. For this purpose, I define the region over which the flux is non zero, ...
14
votes
2answers
1k views

Neumann boundary conditions in NDSolve over nontrivial region

The problem I would like to solve involves diffusion in the following region ...
3
votes
0answers
66 views

Verification of results given by NDSolve

I am trying to solve a system of ODEs using NDSolve. The differential equations used are obtained by applying method of lines to actual governing equation. The system includes differential equations ...
0
votes
2answers
87 views

Matrixform ndsolve for mobile robot dynamic equations

Error is: NDSolve::ndsdtc: The time constraint of 1.` seconds was exceeded trying to solve for derivatives, so the system will be treated as a system of differential-algebraic equations. You ...
15
votes
5answers
15k views

How can I plot the direction field for a differential equation?

I'd like to plot the graph of the direction field for a differential equation, to get a feel for it. I'm a novice, right now, when it comes to plotting in Mathematica, so I'm hoping that someone can ...
0
votes
1answer
51 views

Ndsolve parametricplot

Ndsolve solution cant manipulate parametric plot!! ...
1
vote
0answers
50 views

Transient PDE with a complex boundary condition

I am trying to solve a PDE, but one of the boundary conditions is complex, because it includes an integral over the function that I am looking for. The code is shown below ...
0
votes
2answers
92 views

NDSolveValue and DirchletConditions for cylindrical disk

my aim in this is to model the current flow of a cylindrical disk with one end set to potential 0 and the other end set to potential 1. In this section of code I am trying to find the scalar ...
0
votes
2answers
72 views

Not seeing line defined in an Epilog option

In the following code, the line defined in Epilog option of my 2nd parametric plot doesn't show up in the content pane of my ...
2
votes
1answer
55 views

Problem with NDSolve and Sign

If c1 cnd c2 are zero, the code responds very well; but if one of c1 or ...
2
votes
0answers
102 views

Precision and accuracy in NDSolve and NMinimize

I use NDSolve quite a lot and have noticed that setting values for AccuracyGoal and ...
2
votes
1answer
90 views

Why does NDSolveValue giving crappy results?

I have been trying out mathematica 10 features, but sadly unable to use NDSolve for even simple PDE's. I am still wrestling with the problem of boundary conditions. The solution I get in the ...
6
votes
1answer
118 views

ParametricNDSolve[ ] and NMinimize[ ] in Combination

I have the following code that is used to simulate a spacecraft orbiting Mars, and uses ParametricNDSolve to vary the spacecraft's initial conditions using a parameter value ...
1
vote
1answer
90 views

solving system of non-homogeneous advection equation using mathematica?

This question is followed up from this question How to solve a certain coupled first order PDE system Here I consider the non-homogeneous advection system \begin{equation} ...
3
votes
1answer
98 views

Nonlinear PDE solver

I would like to solve the following nonlinear PDE: $$ \frac{\partial^2 \phi}{\partial x^2} - \frac{\partial^2 \phi}{\partial t^2} = \lambda |\phi|^2 \phi $$ I was trying: ...