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

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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
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1answer
99 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
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0answers
31 views

exe file creation [duplicate]

HOW CAN I MAKE IT exe FILE? PLEASE HELP... ...
4
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2answers
116 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
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2answers
215 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
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1answer
71 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
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1answer
71 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?.
3
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1answer
94 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 T}{\...
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1answer
86 views

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

I used the following equations to solve a structural problem: ...
0
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1answer
69 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
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0answers
51 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 rho[...
0
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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
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2answers
198 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 ...
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2answers
108 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: $f=-1/(2\sqrt{2})$, $...
4
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2answers
80 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
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1answer
84 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
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1answer
89 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
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1answer
87 views

Piecewise function on boundary condition

Consider this initial-boundary-value problem: $$\frac{\partial u}{\partial t}=\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2},\quad \Omega=(0,1)\times(0,1),\quad t>0.$$ $$u(x,0,t)=...
6
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1answer
94 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 ...
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1answer
161 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
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1answer
72 views

Scoping problem with NDSolve [closed]

I'm trying to solve a more complex problem , however , this simple problem can represent well : ...
1
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1answer
159 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
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0answers
104 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
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2answers
361 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 ...
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1answer
63 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
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0answers
102 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: ...
1
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1answer
97 views

Solve differential equations with an initial condition in the form of a limit as $t\rightarrow \infty$

I want to solve the following differential equation with the initial condition This is known as the Bunch-Davies vacuum, and the above are equations (4.1) and (3.37) from this paper Here is ...
1
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1answer
72 views

Trying to Plot Phase Plane of Nonlinear system

I'm trying to graph the phase plane of the following nonlinear system in mathematica using NDSolve, and vectorplot. dx/dt = y dy/dt = x - y + x ^ 3 And this is ...
2
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0answers
70 views

NDSolve produces zombies

I am using Mathematica 10.1 and when I execute NDSolve then there are temporary variables produced every time I call it. This seems not to happen when I explicitly ...
3
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1answer
157 views

Errors Solving Elliptic PDES with FEM

I am trying to solve the equation below governing transversely isotropic plane strain in cartesian coordinates with the given boundary conditions based on code found here using Mathematica 10.1 on OSX ...
1
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1answer
88 views

I was wondering why I got the different answer of the same differential equation in two different ways?

Cross-posted in https://www.zhihu.com/question/40784580 In Mathematica I got the different answer of the same differential equation respectively in analytical method and numerical method. At the ...
1
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1answer
159 views

Problem with convergence of limiting value in Manipulate

I created a nice Manipulate box of the magnetic field outside and inside a spherical shell placed in an homogeneous magnetic field. The code is working great, but it has a problem at a limiting value,...
1
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0answers
62 views

DSolve throws an error about Solve and returns unevaluated [duplicate]

I evaluate: DSolve[{2*y[x] + y'[x]^2 + a*x^b == 0}, y[x], x] During evaluation of In[26]:= Solve::ifun: Inverse functions are being used by Solve, so some ...
0
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1answer
132 views

Solving a nonlinear systems of coupled differential equations with boundary conditions

I am trying to solve the following systems of coupled differential equations with boundary conditions (BC) at $0$ and at $∞$ : $y_{1}'(x)=\frac{-\sqrt{\frac{2}{\pi}}\,\frac{\alpha}{18}\,x^4+x\,y_{2}(...
0
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1answer
111 views

Understanding the symbolic solutions of a system of differential equations

I'm trying to solve a simple system of differential equations but get outputs i just cant grasp, they seem way overkill. Someone said it might be because mathematica interprits the constants as non-...
0
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2answers
98 views

Plotting the solution of a differential equation with its derivative [closed]

The question requires checking of numerical solutions to a differential equation by substituting in those solutions. The original equation is as follows; ...
0
votes
1answer
88 views

ODE system with “parameter” which is a (piecewise) function of one of the dependent variables

I have a 2-dimensional dynamical system where time (t) is the independent variable. My ultimate aim is to perform stability analysis, but I bumped into a problem related to the construction of the ...
1
vote
2answers
65 views

Export NDSolve data

I have calculated a solution of a system of differential equations using NDSolve and generated a plot. How could I extract the data of the solutions? The input is ...
1
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1answer
85 views

DSolve to make the path of a ball in a rotating turntable

I have two equations from a analisys of the following situation. A ball starts to move from the center of a Turntable (rotating disk). I tried to solve these equations on Mathematica but the ...
3
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0answers
197 views

How to solve the Tsunami model and animate the shallow water wave?

Recently when I was learning differential equations, I noticed there is a shallow water wave equation to model the tsunami propagation. How to establish and solve the initial and boundary conditions ...
3
votes
1answer
232 views

How to solve 3D heat equation with Neumann B.C

I'm trying to solve the 3D heat equation on a cuboid to know if all the perimetric surfaces of a Cuboid achieve the desired temperature of a 873K on deadline time of 2 hours. i have convection on all ...
1
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0answers
56 views

NIntegration and DSolve with same variable

I need to solve this problem: Then follows the code, with: ...
7
votes
2answers
339 views

Plotting the image of a curve under a flow

I have some explicit time-independent vector field on the plane, and I would like to study how points evolve under the flow generated by this vector field. The flow is rather complicated and cannot be ...
0
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0answers
63 views

Kovacic's algorithm

Kovacic’s algorithm is used to find out whether or not an ODE has a Liouvillian solution, and if it has, then what that solution is. My question is: Is there any code written in Mathematica for ...
0
votes
1answer
44 views

Getting error when trying to solve two coupled differential equations with NDSolve

Mathematica newbie here. I have been trying to use NDSolve to solve two coupled differential equations. Each equation on its own (minus the coupling terms) solves ...
0
votes
0answers
86 views

Coupled PDEs with discontinuous boundary conditions?

So I have a system of coupled PDEs that represent the movement of an interface of fluid. The interfaces are functions of time and space, ie. $h_1(x,t)$, $h_2(x,t)$, $h_3(x,t)$. The PDEs are horrendous ...
4
votes
1answer
90 views

Solving PDE involving Hilbert transform numerically

I'm trying to solve the following equation numerically: $$u_{tt}-\mathcal{H}(u_x)=A^2_{xx},$$ where $\mathcal{H}$ is the Hilbert transform and $A$ is a prescribed forcing function which we assume ...
1
vote
1answer
227 views

Using the Levenberg - Marquardt algorithm to minimize a user-defined function

I wrote a function in Matlab that optimizes another user defined function using lsqnonlin with 'levenberg-marquardt' option. Now, I'd like to use the first to ...
3
votes
1answer
87 views

Cylindrical GL Equations

I am trying to solve numerically the GL equations in cylindrical coordinates. I already know what the shape of the solutions to these equations should look like, but I am not able to get the correct ...
3
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0answers
85 views

Measuring Temp on a cubical using heat equation with Neumann and Dirichlet boundary conditions

I'm trying to solve 3D heat equation to understand how the temperature varies with time on cubical. i have mixed boundary conditions: Dirichlet on the bottom surface (constant Temp) Neumann on all the ...