# Tagged Questions

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

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### 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. ...
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. ...
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, ...
146 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 ...
209 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 ...
74 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 ...
44 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 ...
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. ...
88 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 ...
31 views

106 views

### Integrating an interpolating function

I have been using the following NDEigensystem command to generate the eigenfunctions of the laplacian with a square domain: ...
205 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 ...
68 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 ...
66 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?.
58 views

### plot for coupled differential equation? [on hold]

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.... ...
88 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: kt\frac{\partial^2 T}{\partial x^2} = \epsilon \sigma T^4, \ \ \ T(0) = T_0, \ \ \ \frac{\partial ...
85 views

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

I used the following equations to solve a structural problem: ...
64 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 ...
44 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 ...
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: ...
195 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 ...
107 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: $f=-1/(2\sqrt{2})$, ...
77 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 ...
77 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 ...
83 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 ...
80 views

### Piecewise function on boundary condition

Consider this initial-boundary-value problem: $$\frac{\partial u}{\partial t}=\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2},\quad \Omega=(0,1)\times(0,1),\quad t>0.$$ ...
89 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 ...
156 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 ...
69 views

### Scoping problem with NDSolve [closed]

I'm trying to solve a more complex problem , however , this simple problem can represent well : ...
150 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 ...
92 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 ...
346 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 ...
62 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 ...
92 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: ...
96 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 ...
70 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 ...
69 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 ...
154 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 ...
85 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 ...
151 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 ...
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 ...
126 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 $∞$ : ...
110 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 ...
92 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; ...
87 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 ...
57 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 ...
76 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 ...
175 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 ...