# Tagged Questions

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

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### Three Body Problem Equilateral Triangle

I'm currently working on showing that the equilateral triangle arrangement of the three-body problem has an analytic solution. So far I've written the equations of motion of each body into Mathematica ...
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### Solution to PDE with “MethodOfLines” is not returning any values

I have been working on this code for quite a while now trying different types of solutions and I cannot get any actual values out of the NDSolveValue function. I have included my code so you can see ...
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### WhenEvent behavior changed from v9 to v10 - how to fix the code?

A couple of years ago I asked a question about solving n-body systems with NDSolve and detecting collisions with WhenEvent. I ...
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### How to put the result of NDSolve in a function?

I have solved an ODE with NDSolve, and put the result in S: S = NDSolve[{y'[x]==(y[x]^4+y[x]+1)^(1/2),y[0]==0}, y, {x, 0, 100}] But i don't want to plot y[x] ...
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### NDSolve with piecewise function gives error “Encountered non-numerical value for a derivative at x == 0.” [duplicate]

I am solving differential equation with piecewise function and i am getting error that NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0.. >...
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### Second order differential equation, with term from previous numerical solution

I have a second order differential equation, in terms of a term that was previously obtained from numerically solving another equation. Numerical solution of equation before 2nd order equation: <...
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### Comparison between numerical solution of nonlinear ode and nonlinear ode of second order

Background Let's consider the following initial value problem for nonlinear system $$\begin{cases} E' &=& 1 - n_e, \\ n_e' &=& -8\,n_e\,E, \end{cases} \tag{1}$$ with the following ...
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### Finding terms of the perturbation solution

I've got a task to find first three terms of the perturbation series solution to: $$y' = 1 +(1+\epsilon)y^2,\quad y(0)=1, \quad t > 0,$$ for a small $\epsilon$. I am supposed to use Mathematica ...
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### How to calculate an average error between numerical and analytical solution of the PDE?

I have second-order initial boundary value problem. Here's my code returning numerical solution (and plotting it). ...
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### Easy way to get the boundary of a geometric object [closed]

I am trying to define von Neumann boundary conditions for a prism. To do so I need the boundary of the geometric object. I can't seem to find an easy way to do this. I have tried to hard code a ...
195 views

### How do I animate a bar chart?

Is there any easy way to have an animated bar chart (one where the heights of the bars change with time)? I currently have the following code: ...
203 views

### Finite element boundary breaking

I am trying to model a cantilever beam which can vibrate. On the left the beam is clamped. I am largely following user21 here and also the example in help. I start by doing a static beam which works ...
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### Error message when using DSolve

I am trying to solve the differential equation $2y^2 + 2 x y y' + x y^3 y' - 2 x^2 (y')^2 + x^2 y y'' = 0$ I tried ...
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### Fitting data using ParametricNDSolveValue and NonlinearModelFit [closed]

I'm trying to evaluate the kinetics of the chemical reaction. For that I need to fit my experimental data to the kinetic equation. These are my steps in Mathematica. ...
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### Numerical derivative of a function which solves a nonlinear system of ODEs

My dear friends, I want to study a nonlinear system of ODEs and to plot a function and its derivative which is defined from the functions of the system of ODE. The question is how to find the ...
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### how to solve nonlinear partial differential equation of fractional order [closed]

How to solve this equation by using homotopy perturbation method with the help of the riemann liouville integral? Based on homotopy technique, this is as far as I can go. Somebody please help me (∂...
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### NDSolve breaking down

I'm trying to model a situation involving charged sphere in a dynamic electric potential, and find out how the rotational motion of the sphere affects the translational dynamics in two dimensions. ...
132 views

### NDSolve: Using time delays in a WhenEvent

I was wondering whether there is a way to use WhenEvent in a system of delay differential equations, for example: ...
183 views

### Finite Element Mass and Stiffness Matrices

I am attempting to use the finite element method to solve a vibration problem. I am following user21's answer from here which is very helpful. My problem is that I am confused by the use of the mass ...
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### Solving a differential equation with a specified “input vector”

I have the following differential equation: ...
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### system of differential equations in Mathematica

How can I formulate the addressed system of differential equations in Mathematica for to find a general solution for $f[x_1, x_2, x_3, y_1, y_2, y_3]$. http://math.stackexchange.com/questions/...
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### Lyapunov Exponent of DDE

What is the procedure to compute Lyapunov exponent for Delay Differential Equation using Mathematica code? If we consider the famous Mackey-Glass Equation: ...
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### Solving ODE in power series about infinity

I want to solve a particular ODE in power series of 1/x. I can obtain the power series solution about x=0. Can any one suggest how to obtain a series solution in 1/x for the following ODE? I tried ...
I'm trying to figure out how is possible to solve a Poisson equation $\nabla\cdot[d(x,y)\nabla u]+1=0$ where $d(x,y)$ equals 1 in one region and 2 in another one. Let say I have homogeneous ...