Questions tagged [differential-equations]

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

1,063 questions with no upvoted or accepted answers
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154 views

Fluid Flow PDE with Mass Conservation

Modeling a simple stepped nozzle for gas flow and having difficulties with the application of the mass conservation equation as part of the boundary conditions. I am following the fluid flow example ...
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113 views

NDSolve can solve two systems of equations separately but not simultaneously

I want to solve a system of coupled equations. After facing problems solving the coupled system, I reduced it to both of the systems uncoupled. Even uncoupled, the equations will not solve ...
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0answers
190 views

Boundary value problem, multiple dimensional shooting, coupled eigenvalue problem

Following the one dimensional boundary value problem here, I would like to understand the easiest way to solve a BVP for a coupled system. In the 1D case, BVP can be converted to an initial value ...
2
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0answers
956 views

how to obtain general solution for Laplace PDE in spherical coordinates using DSolve?

Can DSolve given a general solution to Laplace PDE in spherical coordinates without given boundary conditions? I tried, but not able to get a solution. Do I need ...
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215 views

Where to find LieSymm-PDE Package for Mathematica?

I am unable to find the LieSymm-PDE package for Mathematica developed by Vladimir Pulov et al as outlined on the website: http://www.swmath.org/software/12188 as well as explained in the paper: https:/...
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0answers
459 views

Wormhole embedding diagram

I am trying to reproduce the embedding diagrams for the evolution of a Schwarzschild wormhole described in this paper. Following the paper notation, we denote the Kruskal coordinates by $(v,u)$. For ...
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1answer
446 views

Automatic Boundary conditions in NDSolve

I would like to know what kind of boundary conditions Mathematica implements in NDSolve when not specifying any boundary conditions by hand. So for example solving ...
2
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0answers
357 views

NDSolve Problem with step size and Stiffnes

I need to solve a 5 coupled non-linear differential equation system. There seems to be no apparent singularity but whenever I tried to evaluate the system in Mathematica. It gives the error ...
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0answers
71 views

How to check that a function is solution of an ODE with Mathematica

Let $$S(t)=\int_0^t\int_t^\infty \left(\frac{1}{(1+x^2)^{1/4}(y-x)^{\frac{3}{2}}}-\frac{1}{(1+y^2)^{\frac{1}{4}}(y-x)^\frac{3}{2}}\right)\mathrm d y\mathrm d x.$$ Is there a way to check with ...
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77 views

Confused on the Positionvariables in SymplecticPartitionedRungeKutta Method for NDSolve

I am solving a set of differential equations with symplecticpartitioned runge kutta method. After checking my code for a long time, I found the example code in the tutorial of Mathematica also has a ...
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0answers
264 views

Solving a coupled PDEs using FEM with Robin conditions

The same type of question has been answered here but for single PDE. The main issue I am facing is how to write the weak form for two PDEs. $$\epsilon^2\frac{\partial ^2u}{\partial x^2}+\frac{\...
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0answers
106 views

Difficulty setting a time step or stabilizing the transient heat equation

I have been trying to solve the transient heat equation using finite elements. When I set the thermal diffusivity to a realistic number I get instabilities in the solution. It seems that larger ...
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0answers
319 views

Data fitting with differential equation and non analytical integral

I would like to fit a set of data (measured value vs time) with a model that contains a differential equation and an integral that has to be evaluated numericaly. The integral also contains Bessel ...
2
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0answers
92 views

DEigenvalues with Robin B.C. sign problem

To find eigenvalues for $y''=\lambda y$ with robin boundary conditions on one end, and Dirichlet on the other end, I am getting correct value when robin B.C. on the right side, but when I flip things, ...
2
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0answers
255 views

Solving nonlinear diffusion equation by NDSolve

I have checked all issues regarding to solving nonlinear PDE numerically. I however try to solve following equation via NDSolve function and get some troubles. And this is my code for above-...
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171 views

Solving a couple of PDEs (NDSolve :There are fewer dependent variables, {b[t,y]}, than equations, so the system is overdetermined.)

I'm new to mathematica. I'm trying to solve a couple of PDEs. My code is here. ...
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0answers
217 views

Solving a system of nonlinear PDEs with a piecewise initial condition

I need somw help in using NDsolve. I have a complex system of two PDEs which I am trying to solve numerically (shown in the code below with initial conditions and boundary value condition). I want to ...
2
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0answers
1k views

Plotting the Magnetic Field

I have a dataset of $ \textbf{B} = {B_x, B_y, B_z}$. (Quite a big dataset :78*100*150) I want to plot magnetic field lines. If I was working with an analytical function, the magnetic field line ...
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120 views

Get the parametric equations of the Cycloid

How to get the parametric equations of the cycloid from the following differential equation? ...
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0answers
509 views

Solving the Euler-Lagrange equation with NDSolve`ProcessEquations

I would like to compute the shortest distance between a number on pairs of points on a 2-dimensional Riemanniann statistical manifold (Negative Binomial distributions manifold, equipped with the Rao's ...
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0answers
198 views

Stopping NDSolve ahead of a crash

During the evaluation of an NDSolve expression, when it is known that slope goes to infinity at location $y=1$ in the ODE $$\frac{dy}{dx} = \sqrt\frac {y^2+1}{y^2-...
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0answers
40 views

Improving the speed on an iterated differential system

I'm working on a simulation where I need to solve a differential system for a function, and then use the solution to this system to calculate another function that is used as an input to this ...
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0answers
769 views

Linear tangent steering law and orbital insertion altitude

I've been trying to figure out how to build a rocket launch simulation that allows the user to specify the desired altitude at which a payload will be inserted into a stable circular orbit, but have ...
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0answers
216 views

Modelling heat exchange between flowing fluid and surroundings

Starting from this question: Couple a PDE and ODE in NDSolve I would like to modify the fluid from static to a flowing one in the y direction. that's the original code that I modified a little bit: ...
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0answers
66 views

How to fix a problem like this in NDSolve?

I am a beginner on Mathematica. Now I am trying to solve second-order PDEs using NDSolve. But I encountered the following error. Could anyone help me find out the mistake I made? Thank you in ...
2
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0answers
264 views

Solving Differential Equation for derivative

I am new to mathematica and am trying to solve a differential equation. Actually, I am not entirely sure if the system can be called differential equation. I am interested in finding out the second ...
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0answers
249 views

NDSolve with only discrete variables

Is is possible to use NDSolve with DiscreteVariables if there are no continuous-time variables? This fails: ...
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0answers
223 views

How to change the boundary condition near singularity

The following system has a singularity around $x=0.451$. What I want to do is to detect when the solution gets close enough to this singular point (in this example I'm using the threshold of $0.001$), ...
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96 views

NDSolve problem in Mathematica 10.1, possible bug

The following code, ...
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0answers
150 views

Unusual error message from Solve when called by DSolve

Question 111150 presents an equation nonlinear in its leading derivative ...
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0answers
85 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 ...
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0answers
158 views

NDeigensystem returns error due to mesh discretization when calculating vibrations of a cantilever

There was an transcription error in the code I provided in a previous post: https://mathematica.stackexchange.com/questions/105713/ndeigensystem-returns-complex-non-hermitian-error-for-the-...
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0answers
146 views

Bypassing a Singularity

I am having trouble trying to solve an ODE that has a singularity when the function M[x]=1. Basically the denominator has ...
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0answers
117 views

Eliminating instabilities in a transient finite element solution at a discontinuity near t = 0

I have found a transient solution to the 1D heat equation where the initial condition is discontinuous. The results are accurate except for when time is small. The initial condition looks like this: $...
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0answers
83 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 ...
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133 views

Numerical Analisys and StepDataPlot

I'm using StepDataPlot to compare several methods for differential equations. Does exists a function, or something else, to find the number of steps that the choosen method used to find the numerical ...
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0answers
277 views

Solving 4 coupled differential equation for modelling boson star

I'm trying to study about modelling star from a journal. To get the characteristics of the star, I have to solve 4 differential equations which are coupled each other. I want to use Mathematica 9 to ...
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0answers
321 views

How to Implement a “Function Object” suitable for NDSolve and Finite Element Method?

I have a bunch of methods that shoud return an expression that behave like a function, i.e. an expression that, when supplied with suitable arguments, evaluate to something. A simple ...
2
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0answers
287 views

Solving non-linear coupled ODE with constraint using NDSolve

I am trying to use NDSolve in Mathematica to solve the following coupled ODEs from a paper I am trying to understand. I have the following 5 differential equations: ...
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0answers
523 views

Failing to solve a simple PDE with NDSolve

I'm trying to solve the following PDE. Actually this is a major simplification of the original with all x,z dependent coefficients being fixed. For some reason Mathematica (10.0) cannot solve even ...
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0answers
234 views

How to handle solution returned by ParametricNDSolveValue in FindRoot

i was trying to solve a problem relative to root finding in a system of differential equations; here's a simpler case. With two distinct set of parametric differential equations, i'm able to find the ...
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0answers
1k views

Linear System with Complex Eigenvalues

My students will need to do the following work by hand. \begin{align*} x_1'&=-\frac14x_1+2x_2,\quad x_1(0)=1\\ x_2'&=-8x_1-\frac14x_2,\quad x_2(0)=1 \end{align*} They set it up in matrix form....
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0answers
420 views

System of Partial differential equations

I am trying to solve numerically a system of 3 partial differential equations and I am facing a problem. My functions are f[x,t], ...
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0answers
93 views

DSolve solution of two unknowns

I have one problem with the solution of the system of two differential equations. I waited hours, but Mathematica didn't give me a solution. Is there any way to obtain the results if we suppose that ...
2
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0answers
1k views

NDSOlve - 1D wave equation with boundary

I am currently trying to solve the 1D wave equation with Mathematica: $$c^2\frac{\partial u}{\partial x^2}=\frac{\partial u}{\partial t^2}$$ I want to do so for a cantilever with a tip mass: One ...
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0answers
252 views

How to solve Fuzzy Differential Equations

How to solve Fuzzy Differential Equations using DSolve or NDSolve, Or Differential Equations with fuzzy number as initial conditions
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2k views

NDSolve and strange “nonlinear coefficients problem”

I'm stuck solving the following problem. I defined two functions as follows: $$ \varphi(\lambda) = \frac{\left((\lambda-2)^2-1 \right)^2}{4}$$ $$ \gamma(\lambda) = \varepsilon^2 \quad\text{where}\...
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0answers
884 views

NDSolve error message: Cannot find starting value for the variable y'

I'm attempting to solve a differential equation using NDSolve. This is the code: ...
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0answers
96 views

Can't find the limit of this complicated expression

Here is the limit I am trying to calculate ...
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0answers
449 views

PDE with Integral constraint

I am trying to solve the Non-linear Schrodinger equation $-\Delta \psi(r) + \psi(r) - |\psi(r)|^2\psi(r) = 0$ where $r \in \Omega$ In a square domain ($(x,y) \in \Omega$ where $\Omega=[0,1]\times [0,...

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