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

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9
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1answer
157 views

Kernel Crash while using “ValuesOnGrid” method of InterpolatingFunction

Bug introduced in 10.0.0 and fixed in 10.2.0 I was experiencing some kernel crash while using "ValuesOnGrid" method of an ...
9
votes
2answers
388 views

Differentiating an unknown solution to a PDE

Sorry if this question is too basic -- I'm not very familiar with Mathematica. I am interested in a way to systematically address the following sort of problem: Suppose that $u=u(x,y)$ is a function ...
9
votes
1answer
654 views

Complex valued 2+1D nonlinear PDE using NDSolve

I am trying to follow the main ideas presented in this question, applying it to my own problem, which is a complex, time-dependent, nonlinear PDE: $$i \frac{\partial \psi}{\partial t} = \left[ ...
9
votes
1answer
336 views

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

We know that changing the option InterpolationOrder in ListLinePlotListPlot3D、...
9
votes
1answer
207 views

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 ...
9
votes
1answer
909 views

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 ...
9
votes
1answer
859 views

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 ...
9
votes
1answer
1k views

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: ...
8
votes
2answers
6k views

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 ...
8
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2answers
517 views

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: ...
8
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2answers
935 views

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. ...
8
votes
2answers
796 views

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 ...
8
votes
2answers
2k views

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 ...
8
votes
2answers
714 views

Nonrectangular region for NDSolve

I have a PDE with mixed boundaries (Neumann and Dirichlet on some sides) in the region $(t,x,y) \in \left( 0, T\right) \times\left\{ -L \leq x \leq L, 0 \leq y \leq h(x) \right\}$ where $h(x)$ is ...
8
votes
2answers
494 views

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 ...
8
votes
3answers
160 views

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 ...
8
votes
1answer
895 views

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 ...
8
votes
2answers
419 views

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 ...
8
votes
1answer
119 views

Beam deformation due to localized force distribution

I would like to simulate the deformation of a beam which is fixed on one end and has some localized forces applied along the top. I have been inspired by this Mathematica example: ...
8
votes
1answer
360 views

Diverging solution to coupled second order ODEs from NDSolve

For a physics application I am considering the radial Bogoliubov-de Gennes equations in two dimensions. In dimensionless form they read as follows $$ \begin{cases} ...
8
votes
1answer
408 views

How can I improve speed of code that generates an orbit plot?

I am attempting to generate an orbit for the "time 2 Pi map" of a forced damped pendulum. The example comes from page 57 in the Chaos text by Alligood,Sauer and Yorke, see Figure 2.7. The code ...
8
votes
2answers
1k views

Driven simple harmonic oscillator — amplitude of steady state motion

I am (partly as an exercise to understand Mathematica) trying to model the response of a damped simple harmonic oscillator to a sinusoidal driving force. I can solve the differential equation with ...
8
votes
1answer
190 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 ...
8
votes
1answer
474 views

Optimizing Monte Carlo simulation of a Pred-Prey model

My assignment and code As part of an assignment for one of my classes, I'm trying to run a "massive" Monte Carlo simulation in Parallel on the follow model: ...
8
votes
3answers
960 views

Can Mathematica solve this sort of functional/differential equation?

I am looking for differentiable functions $f$ from the unit interval to itself that satisfy the following equation $\forall\:p \in \left( 0,1 \right)$: $$1-p-f(f(p))-f(p)f'(f(p))=0$$ Is there a way ...
8
votes
1answer
140 views

NDSolve`FiniteDifferenceDerivative gives wrong result when the precision is not MachinePrecision

Bug introduced in 8 or earlier and persists through 10.3.1 I want to get a pseudospectral differentiation matrix by NDSolve`FiniteDifferenceDerivative. ...
8
votes
1answer
205 views

SymplecticPartitionedRungeKutta shows strange error

Bug introduced in 9.0 or earlier and persisting through 10.2 or later I tried to solve Hamiltonian system ($Q$ is a vector of all generalized coordinates, $P$ - of generalized momentum) $$ ...
8
votes
1answer
991 views

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 ...
8
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1answer
503 views

Setting the DifferenceOrder Option

I've been playing around with Method in NDSolve[...] and can't quite seem to figure out how to force ...
8
votes
1answer
71 views

How can I identify which solution triggered the WhenEvent?

I am using NDSolve for problems like this: ...
8
votes
1answer
208 views

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: ...
8
votes
1answer
223 views

Curious solutions of x' = Sqrt(x), x(0)=4

Consider the solution of $x'=\sqrt{x}$, $x(0)=4$ using DSolve. ...
8
votes
1answer
1k views

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 ...
8
votes
1answer
197 views

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 ...
8
votes
1answer
444 views

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) ...
8
votes
1answer
177 views

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 ...
8
votes
1answer
129 views

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 ...
8
votes
1answer
258 views

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 ...
8
votes
1answer
69 views

Working Precision in nonlinear control systems

When simulating a nonlinear control system using StateResponse , do the options WorkingPrecision, ...
8
votes
0answers
2k views

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|) ...
7
votes
3answers
3k views

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 ...
7
votes
2answers
1k views

Creating Plots for a Family of Solutions

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: $u_n(r,t) = [a_n\cos(k_n\alpha t)+b_n\sin(k_n\alpha t)]J_0(k_nr)$ ...
7
votes
2answers
479 views

Click in a vector plot to plot several solutions of a system of differential equations

I am aware of the Locator button and I am aware of the Equation Trekker package, but they are not what I want to use. Here is what I specifically want to know how to do, if possible. Consider the ...
7
votes
2answers
224 views

Extending NDSolve beyond a singularity

The $\tan$ function satisfies the following IVP: $$y'=1+y^2 ,\quad y(0)=0 $$ and has simple poles at the points $x=\pi/2+ \pi n$ for integer $n$. When trying to get $\tan$ via numerical ...
7
votes
2answers
332 views

Plotting the image of a curve under a flow

I have some explicit time-independent vector field on the plane, and I would like to study how points evolve under the flow generated by this vector field. The flow is rather complicated and cannot be ...
7
votes
2answers
1k views

Solving the Helmholtz equation in polar coordinates

I'm trying to (as a simple starter) find the solution to Helmholtz equation in polar coordinates -- I already know what it is and can derive it by hand, but just want to start here before asking ...
7
votes
3answers
3k views

Lyapunov Exponent

Does anyone know a (simple) Mathematica code for computing the Lyuponov Exponent for the Rossler System? Thank you Rossler System: ...
7
votes
2answers
255 views

Solve a time-dependent matrix DE using NDSolve

I am trying to numerically solve a time-dependent matrix DE using Mathematica. However, it seems that Mathematica freezes even for two-dimensional matrix equations. For example, we have: ...
7
votes
3answers
426 views

Envelope for harmonic oscillator [duplicate]

I am able to take the expression $\cos 11t-\cos 12t$ and use the sum to product identity to write it in the form $$\left(2\sin\frac t2\right)\sin\frac{23}{2}t.$$ I can then plot the function and use ...
7
votes
2answers
3k views

how to solve ODE with boundary at infinity

y''[x]-x y[x]==0 y[0]==AiryAi[0], y[infinity]==0 the analytic solution to this ODE is the Airy function y[x]=AiryAi[x] if I ...