# Questions tagged [differential-equations]

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

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### Speed up a differential equation solution + parameter integration + parameter maximization

The problem I am trying to solve can be described as a maximization of an integral of the solution of a differential equation. A MWE is ...
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### Problem with stopping NDSolve after a condition is met

I'm trying to write a piece of Mathematica code that is essentially a differential equation solver that needs to take a specified function $V[t,q]$, and then numerically solves the differential ...
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### Code to find the Covariant Lyapunov Vectors

I've been able to find a decent amount of existing resources for computing the Lyapunov Exponents for a system of differential equations. Is there any existing code/resources for computing the ...
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### Solving a Modified Biharmonic Equation on a Square

I am seeking to solve the differential equation \left[\partial_{\overline{x}}^{4}+2\left(1+\delta\right)\partial_{\overline{x}}^{2}\partial_{\overline{y}}^{2}+\partial_{\overline{y}}^{...
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### DSolve[] and initial conditions

Take some simple function of 2 variables, e.g. f[x_,y_] := x+y and try to solve a PDE of it for the general solution: ...
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### Is this the expected EvaluationMonitor behavior with NDSolve with Method->“SymplecticPartitionedRungeKutta”

It appears that EvaluationMonitor is not being called as expected, but only when I am using SymplecticPartitionedRungeKutta. Here is a stripped down example to illustrate. Forces in Hamilton's ...
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### Quasi-periodic boundary conditions

I am trying to solve the following problem using Mathematica's NDSolve $$\partial^2_{y}\psi+\partial^2_{x}\psi-2\,i\,q\,B\,y\,\partial_{y}\psi-q^2B^2y^2\psi+q\,B\,\psi=0$$ subject to the boundary ...
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### System of PDEs with delay, MapThread error

I have the following code: ...
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### NBodySimulation: custom pairwise potential

I'm trying to define a Lennard-Jones potential in 2D for NBodySimulation ...
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### NDSolve and DSolve solutions

Sorry for this probably trivial question, but I'm at a loss with this simple problem and the way Mathematica handles it. It's about a free-falling object, dropped by a height of 10, starting with zero ...
118 views

### Phase portrait of n-dimensional state-space system

It is usually not difficult to study the state space for n = 2,3 variable states. What if these variables are more than 3, for example 4,5 or 6? There is a rule according to which the dynamic features ...
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### How to get the NDSolve to seek only a real solution?

I use NDSolve to solve system of 2 ODE of 1st order: ...
203 views

### Solving for a minimum action path in mathematica

I am interested in computing a quantity that is mathematically defined as follows, $$\phi(x_1,x_2) = \inf_{T>0} \inf_{\gamma \in C^{x_2}_{x_1 }(0,T)} \int_{0}^T L(\gamma, \dot{\gamma})\mathrm{d}t$$...
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### Nonlinear, second order system of ODEs not solved by Mathematica, solution however exists

I am currently working on solving a system of two coupled nonlinear second order ODEs. I have already shown by hand, that 2 real solutions, as polynomials of second order, exist but I want to use ...
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### Is Inactive Form avoidable when using NDSolve for non-linear ODEs

So this is basically the same question as here referring to information provided here. However, I am wondering if this inactive form is always necessary or more of a convenience. For example, ...
127 views

### Solar System N body Simulation

This is an N-Body simulation for the Sun and the following planetary bodies: Mercury, Venus,Earth,Mars,Jupiter,Saturn,Uranus,Neptune and Pluto. Initial Parameters ...