Tagged Questions

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

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Solving this equation with NDSolve

I'm trying to solve a differential equation numerically. I've written this code but it is leading to some errors "initial history needs to be specified for all variables for delay-differential ...
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Plot Piecewise does not work with NDSolve, works with ordinary function [closed]

How to join output from NDSolve with another function in a plot, using Piecewise or something else? I could join a simple function with another in a plot, but could not do it for the output. MWE: <...
51 views

Eliminate a variable from a differential equation and an algebra equation then collect the remaining variables

Recently, I am attempting to eliminate a variable from a differential equation (DE) and an algebra equation (AE), then collect the remaining variables as a new (grand) parameter. Actually, I have ...
122 views

Plotting two variables indirectly dependent on each other

I have the following system of linear ODEs for "i" number of species "c" migrating in "j" number of habitats: ...
133 views

Time-dependent pde with periodic boundary conditions - NDSolve gives incorrect results

I'm trying to solve very simple differential equation with perdiodic boundary conditions and non-constant initial condition, however the results I'm getting don't seem to be correct. Here's my code: <...
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Plotting data from a Table in Mathematica

I have been able to solve some differential equations using Tables. The code works fine without errors. However, I am unable to plot the results. Any help would be appreciated. ...
136 views

NDSolve::depdole error

I'm trying to solve a pair of differential equations with NDSolve. They contain a discontinuous function bounce. I've trimmed ...
186 views

How to work with ParametricNDSolve?

Update 3: I got it. A small dumb mistake... It has to be Evaluate[xP[y]'[0] /. s10] like this. Oh well... Update 2: So if do this ...
139 views

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 ...
61 views

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 ...
135 views

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] ...
321 views

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.. >...
33 views

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 ...
102 views

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 ...
100 views

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). ...
79 views

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 ...
192 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: ...
201 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 ...
86 views

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 ...
87 views

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. ...
38 views

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 ...
54 views

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. ...
127 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: ...
173 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 ...
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/...