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

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-3
votes
1answer
78 views

How to implement Bifurcation of delayed Lorenz system? [closed]

The delayed Lorenz system is as follows: (Bifurcation parameter as $\tau$) $$\begin{align*} D^\alpha x_1(t) = & a_1(x_2(t-\tau)-x_1(t)) \\ D^\alpha x_2(t) = & a_2x_1(t)-x_2(t)-x_1(t)x_3(t) ...
5
votes
1answer
81 views

Passing starting values to FindRoot when called by the Shooting Method of NDSolve

According to the documentation of the NDSolve Method -> "Shooting" option, it is possible to pass to ...
0
votes
0answers
88 views

NDSolve with default settings solves much faster than classic Runge-Kutta 4

NDSolve with default parameters takes 0.25 s for the first run. With Runge Kutta 4 specified, it takes about 4.6 s, ...
0
votes
0answers
65 views

How to systematically approach when solving a large system of differential equations?

I defined several functions in order to get to the final system of a partial differential equations I have to solve. Here is how I did those definitions: ...
0
votes
1answer
80 views

Proper way to produce StreamPlot

I have faced with problem of not completely correct phase trajectories of ODE, which was produced by StreamPlot. Next following code ends up with this plot: ...
3
votes
0answers
55 views

Singularity treatment in a simple problem [duplicate]

With a simple search, several posts can be found on treating singularities encountered while using NDSolvefamily of numerical methods. However, most of them involve ...
1
vote
1answer
70 views

Discontinious Boundary condition NDsolve

Assume we have any PDE to be solved on the rectangular domain $0<X<4$ and $0<y<2$ How do we tell Mathematica to impose the following boundary conditions? $U[0,y,t]=0, if, 0<y<1, ...
1
vote
2answers
64 views

If statement, differential equation

I've got problem with If statement. It doesn't work. I've never used Mathematica before, probably it's a problem with syntax. ...
1
vote
0answers
34 views

wrong sign with NeumannValue

I want to use NDSolveValue with Neumann boundary condition. The documentation says this https://reference.wolfram.com/language/ref/NeumannValue.html . In the ...
1
vote
2answers
233 views

Differential equation and For loop in Mathematica

I'm trying to optimize some kind of process in Mathematica. I did it without any problems in Matlab and now I'm trying to do the same in Mathematica which I don't know at all. I'm trying to find the ...
1
vote
1answer
77 views

How to plot an Ordinary differential equations

Hey guys I'm using mathematica 5 now, and so new to this software thing. May I know how to plot the direction field using PlotVectorField[] and also finding ...
1
vote
0answers
41 views

NDSolve with (approximately continuous) Piecewise input

I am finding some troubles when using NDSolve with this piece of code: ...
0
votes
1answer
30 views

WhenEvent StopIntegration not working [closed]

I am trying to use a WhenEvent to StopIntegration when Tmelt=1356 is reached. Although the NDSolve appears to be working, "StopIntegration" is not stopping the integration and no value is given for ...
3
votes
1answer
69 views

NDSolve with an interpolating function in Piecewise

Again I have question I hope someone can answer. I made a very simple example illustrating my more difficult problem. I want to solve a differential equation numerically with a conditional in the ...
3
votes
4answers
220 views

Stiff coupled system of ODE's

I am having trouble with a possible stiff nonlinear system of ODE's. ...
0
votes
1answer
98 views

NDSolve coupled Non Linear differential equation, Obtain solution

Trying to solve a coupled differential equations of motion. When there is no Working Precision mention it runs and give following plot for θ[t] but this is wrong, θ must be symmetric about 0. ...
0
votes
0answers
25 views

Discretization of a region for NDSolve using [duplicate]

I would like to mesh the region below in order to use it for a calculation by means of NDSolve. Could anyone help me to discretize this region for NDSolve using. Thank you very much. ...
2
votes
1answer
84 views

System of differential algebraic equations with one of the variables as an argument of the other varaibles

This is my first question here and I don't even know what to search for to find a solution. So I'd appreciate it even if someone can point me in the right direction. EDIT: My post had many problems, ...
6
votes
3answers
141 views

Force WhenEvent to respect default stepsize

I have to numerically integrate an equation system and monitor the accumulating datapoints. For example, I fit a line to a subsample of the points and terminate via ...
6
votes
0answers
198 views

Problems with NDSolve for solving coupled Schrödinger-like PDEs with perfectly matched layer boundary condition

I'm trying to solve a full-vectorial wave equation for an arbitrarily shaped wave guide, by using NDSolve and perfectly matched layer (PML) conditions. The PML ...
0
votes
1answer
71 views

Difficulty using NDSolve

I am tying to solve two differential equations with two delays numerically. The result didn't come out and it was written that “NDSolve::ndsz:...step size is effectively zero; singularity or stiff ...
0
votes
0answers
40 views

Problems solving differential equation with ParametricNDsolve for certain parameters

I'm working on a simulation of a physical problem for a few weeks now and I'm starting to get really frustrated about it. The problem itself is the stationary case of the heat diffusion equation in ...
0
votes
0answers
22 views

The result didn't come out and it was written that “step size is effectively zero; singularity or stiff system suspected” [duplicate]

I am tying to solve two differential equations with two delays numerically. The input is given by the picture below. I have tried the methods that have been posted in the web but it didn't work. ...
0
votes
1answer
86 views

How to prevent extrapolation in Manipulate? [duplicate]

How can I limit the time slider to the NDSolve solution range in a Manipulate box, so no extrapolation is used ? More specifically, here's a stripped down version of my Manipulate code which shows ...
2
votes
0answers
31 views

exe file creation [duplicate]

HOW CAN I MAKE IT exe FILE? PLEASE HELP... ...
4
votes
2answers
103 views

Integrating an interpolating function

I have been using the following NDEigensystem command to generate the eigenfunctions of the laplacian with a square domain: ...
4
votes
2answers
203 views

General solution for a linear ODE set with complicated coefficient

This is the original problem that motivated me to ask this question. I encountered it when trying to reproduce the deduction in this paper. (I'll paste the relevant part below to make this question ...
2
votes
1answer
66 views

NeumannValue and FiniteElement Methods : BC not respected

I have noticed on several of my personal cases some issue with the BC using NeumannValue. Let me illustrate the problem. I take the 1D example of ...
0
votes
1answer
62 views

Can i get step by step calculation of results obtained in mathematica? [duplicate]

In mathematica we generally obtain direct result instead of step by step analytical calculation. Can we somehow obtain these steps?.
0
votes
0answers
52 views

plot for coupled differential equation?

I have two coupled equations and sol is written in term of function as shown below. but not getting any kind of plot. Can any one help please. Thanks.... ...
3
votes
1answer
85 views

Trying to find a temperature profile with a nonlinear 2nd order ODE. NDSolve very sensitive to seemingly arbitrary constant

I am trying to solve this differential equation for a heat transfer problem: \begin{equation} kt\frac{\partial^2 T}{\partial x^2} = \epsilon \sigma T^4, \ \ \ T(0) = T_0, \ \ \ \frac{\partial ...
0
votes
1answer
83 views

How to implement NDsolve for thermo structural code? finite - element - method

I used the following equations to solve a structural problem: ...
0
votes
1answer
62 views

NDSolve Surface Plot to Compare Initial Values

I am trying to solve a system of differential equations which model reaction kinetics using NDSolve. I would like to generate a surface-plot of the function value as a function of time and the initial ...
2
votes
0answers
42 views

Boundary conditions (periodic/anti-periodic) for diffusion equation and NDSolve

I am trying to solve a simple diffusion equation in Mathematica. The problem is inspired by spin diffusion, which is why I consider an initial condition that has both positive and negative density ...
0
votes
0answers
36 views

How to specify in NDSolve that the sought function is holomorphic?

If I include the Cauchy-Riemann equations condition in complex form for the sought holomorphic function gf in NDSolve like this: ...
3
votes
2answers
192 views

Plotting the solutions of $y' = -\frac{\cos y}{\sin x}$

I struggle with the problem of plotting the solution of this ODE: $\qquad y' = -\frac{\cos y}{\sin x}$ I've already tried to use ContourPlot in a loop and in a ...
1
vote
2answers
105 views

DSolve doesn't give all the solutions

I'm trying to solve the following ODE $\frac{df}{dx}=-\sqrt{2}\left(\frac{1}{4}-2f(x)^{2}\right)$ In the text where it appears, the authors make a distinction into three cases: $f=-1/(2\sqrt{2})$, ...
3
votes
2answers
75 views

Force ExplicitEuler Method of NDSolve to produce simple “connect the dot” plot

The code plots the solution to an ordinary differential equation (ODE) on its corresponding vector field by one of two methods: (1) click on an initial point of the vector field or (2) keyboard entry ...
3
votes
1answer
73 views

How to eliminate an independent variable from two coupled differential equations?

I want to solve following differential equations using mathematica (I know the solution as it is easy to compute): $$\dot{r}^2+r^2\dot{u}^2=2\kappa^2\frac{1}{r}+h,$$ $$r^2\dot{u}=c.$$ To computer the ...
1
vote
1answer
82 views

Ugly rendering of curve with ParametricPlot3D and NDSolve [closed]

I frequently have this rendering problem when I plot a complicated curve with ParametricPlot3D, found by solving a differential equation with NDSolve : The curve should be more "regular" (it is ...
1
vote
1answer
75 views

Piecewise function on boundary condition

Consider this initial-boundary-value problem: $$\frac{\partial u}{\partial t}=\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2},\quad \Omega=(0,1)\times(0,1),\quad t>0.$$ ...
6
votes
1answer
87 views

How correctly use WhenEvent to detect when gradient is over a certain value?

So I wish to stop integrating my PDE when the spatial gradient is larger than some value, let's say 10. That is to say, my WhenEvent condition wants to be stop when the the maximum gradient over all x ...
1
vote
1answer
154 views

Boundary Problems

I am trying to study what happens to a wave as it passes different boundaries. This is the working wave equation defined on a plane ...
2
votes
1answer
69 views

Scoping problem with NDSolve [closed]

I'm trying to solve a more complex problem , however , this simple problem can represent well : ...
1
vote
1answer
144 views

Solving an ODE with boundary conditions at infinity and 0//different problems [closed]

I am new to this forum, mathematica and I am also not an expert in solving differential equations. With respect to F I want to solve the following differential equation with boundary conditions at 0 ...
3
votes
0answers
84 views

Implementing the Numerov method for solving ODEs with NDSolve

I'd like to implement the Numerov scheme for solving an ODE (Scroedinger Eq time-independent) with NDSolve. I tried in analogy with the Runge Kutta example in the ...
6
votes
2answers
335 views

Piecewise differential equation

Say I have a very trivial function $$ V\left(r\right)=\begin{cases} -V_{0} & 0\leq r\leq R\\ 0 & r>R \end{cases} $$ with $V_{0}>0$ and $R>0$. I would like to let Mathematica solve ...
-1
votes
1answer
61 views

Why does this while-loop not run? [closed]

I would like to solve a set of differential equations numerically. During the process I need to use a discrete variable to annul one of my integration variables. But I also need to control what ...
1
vote
0answers
91 views

How to find the eigenvalues of a custom operator using NDEigensystem? [closed]

I would like to solve a Hamiltonian presented by a 2x2 matrix. Hamiltonian is given by: ...