# Tagged Questions

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

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### The only usage for the option InterpolationOrder in NDSolve is to be set to All?

We know that changing the option InterpolationOrder in ListLinePlotListPlot3D、...
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### How to tell mathematica not to resolve stiffness issues

Very often I solve partial differential equations that are nonlinear and could be up to 4th order. In these cases, it is usual for the solution determined by NDSolve...
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### DSolve documention on web differs greatly from distributed MMA 10.2.0 version

In the course of improving my answer to 95361, I noticed that the DSolve documentation on the web is much better written than that distributed with Mathematica 10.2....
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### how to simplify large expression with lots of special functions in it (BesselY, Hypergeometric, MeijerG etc…)

I saw this DE in Maple forum. When solving it using Mathematica 9.01, even though the result was correct (both solutions gave the same numerical answer for some random values), Mathematica's answer ...
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### NDSolve::ndcf: Repeated convergence test failure. How to solve?

I am trying to simulate a system of $n$ pendulums with some friction in Mathematica 9. This is the code I am using: ...
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### Creating a 3D List Line Plot From Discrete Points

Given the following Runge-Kutta ODE solver and the graphical output below, how do I get a 3D line plot instead of a 3D point plot? I see that there is no ListLinePlot3D function, so I thought it might ...
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### Solving a system of ODEs with the Runge-Kutta method

I´m trying to solve a system of ODEs using a fourth-order Runge-Kutta method. I have to recreate certain results to obtain my degree. But I'm a beginner at Mathematica programming and with the Runge-...
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### Lagrangian to Hamiltonian

I want to go from Lagrangian description to Hamiltonian one. Using the example given by Mathematica I do something like: ...
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### How to solve the differential equation with Duhamel's integral?

How do I solve a differential equation with Duhamel's integral? I tried to solve it with NDSolve, but failed: ...
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### StreamPlot for Bifurcation Diagram

When we do a StreamPlot, I want to show the bifurcation when $a = 0$ transitions to $a >0$, but do not see a better way to do this than the following. ...
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### Finding a 3d curve from torsion and curvature with NDSolve

I'm trying to use the Frenet–Serret formulas to find the curve that matches the torsion and curvature I specify numerically with an InterpolatingFunction. The ...
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### NDSolve with vectors

I'm stumped. I'm trying to write this using vectors, but the 2nd derivative isn't being expanded like I expected it to be. This is a system of equations for a projectile with quadratic drag and ...
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### Catching only the first event in NDSolve EventLocator

I have a system of ODEs that I solve. During the integration process, there's an event that I want to catch, but I want to (a) continue the integration after the event and (b) catch only the first one....
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### DSolve—different solutions for same set of equations using different symbols?

I happen to find that DSolve can give different solutions, even a different number of solutions, for a set of differential equations just by making a change in the ...
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### Animated Wave propagation using split operator method

Here is the state of the art: By solving the time-dependent Schrödinger equation, one obtains that the propagated wave function after time step $\Delta t$ can be calculated by applying the time-...
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### Problem when defining function through NIntegrate and NDSolve and Interpolation - Bug?

More than a single question, I have some doubts about the output of certain functions when defined through the result of other calculations. I am an active user of Mathematica, but maybe I haven't ...
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### 1D Euler Equations

Is it possible to accurately solve the 1D Euler equations in Mathematica using NDSolve? For example, let us consider the problem given here: http://www.csun.edu/~jb715473/examples/euler1d.htm Using ...
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### Setting the DifferenceOrder Option

I've been playing around with Method in NDSolve[...] and can't quite seem to figure out how to force ...
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### PoincareSection for a driven damped pendulum is not generating a Poincaré section at all, why?

So I have the general code from the PoincareSection documentation that is changed up for a Driven Damped Pendulum: ...
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### Curious solutions of x' = Sqrt(x), x(0)=4

Consider the solution of $x'=\sqrt{x}$, $x(0)=4$ using DSolve. ...
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### How to correctly use DSolve when the force is an impulse (dirac delta) and initial conditions are not zero

DSolve (and NDSolve) return different and unexpected solution to differential equation when the input is an impulse. This is ...
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### Controlling the time step in NDSolve?

I generally use NDSolve for stiff non linear partial differential equations of 4th order. I find that a BDF1 method generally does well to placate my beast of a PDE. I've also tried out ...
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### DSolve giving strange error messages solving a PDE

Bug introduced in 6.0 or earlier and fixed in 10.1 Consider this set of PDE $$\left( x^{2}+y^{2}\right) \dfrac {\partial u}{\partial x}+n x y\dfrac{\partial u}{\partial y}=0$$ have general solution ...
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### Issue with the NDSolve code

With this procedure, one may determine an eigen-value function $R(a)$ for any given $\Xi$ (say 0, 25, 50, 75, 100) ...
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### Bug? Problem with derivative of interpolating function from FEM

Bug introduced in 10 or earlier and fixed in version 10.4 I am really not sure if this is a bug or I am missing something very trivial. QUESTION: What I am missing in order to obtain the partial ...
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### What should I learn from DSolve working better with a named constant than a number in this case?

I have an equation $$\bigl(r''(\phi)r(\phi) - r'(\phi)^2\bigr)\bigl(b + r(\phi)\bigr) = r(\phi)\bigl(r'(\phi)^2 + r(\phi)^2\bigr)$$ Here $b$ and $r$ are lengths, and $\phi$ is an angle (in radians, so ...
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### Using a Mathematica index as a DiscreteVariable in NDSolve when solving a coupled set of ordinary differential equations

Context Since the explanation below of the problem to be solved is lengthy, let me preamble this by saying that I have code that works to solve the problem, but I don't know whether (1) it's ...
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### Working Precision in nonlinear control systems

When simulating a nonlinear control system using StateResponse , do the options WorkingPrecision, ...
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### NDSolve and memory usage

After some googling, i've found similar problems around, but didn't find a 100% satisfactory answer, so let me ask here: I'd like to solve a 1+1 problem using the method of lines. In spherical ...
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### Integro-differential equation [closed]

I have to numerically solve a nonlinear partial integro-differential equation using Mathematica. This is my equation, \frac{\partial y(x,t)}{\partial t}=\int_{-\infty}^\infty K_0(|x-u|) \frac{\...
I am wondering how do you set the parameters appropriately for $a_n,\,\alpha,\,\text{and }b_n$ to plot the family of solution of: $u_n(r,t) = [a_n\cos(k_n\alpha t)+b_n\sin(k_n\alpha t)]J_0(k_nr)$ ...