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

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How to use results of NDsolve[] for further solving of ODEs?

I have a system of ODEs with 10 eqns. I can solve the first 5 independently. How can I use those results to solve for the remaining 5? An easy example would be $\dot{x}=f(x), \quad \dot{y}=g(x,y)$ ...
7
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3answers
358 views

How to prevent instability blow up in NDSolve?

I have the following code to solve a PDE: ...
7
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1answer
672 views

Getting clearer StreamPlot output

When I do a StreamPlotof a rather complicated pair of differential equations, it loses some details. For example: ...
7
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3answers
291 views

Find the eigenvalues for an ODE

For example, say I have $y'' + \lambda y = 0$ and the endpoint conditions are $y'(0) = 0$ and $y'(\pi) = 0$. How can I find the values for $\lambda$ that for which there is a non-trivial ($y\neq0$) ...
7
votes
2answers
550 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 ...
7
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2answers
894 views

How to set the NDSolve method to LSODA

I notice that off all the Method options available for NDSolve[...], LSODA is invoked quite ...
7
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2answers
160 views

Clicking phase plane with mouse

Here is what I have thus far: ...
7
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2answers
553 views

Only final result from NDSolve

Finally I started to play with differential equations in Mathematica. And I have faced the problem, which seems too me so basic that I'm afraid this question is going to be closed soon. However, ...
7
votes
2answers
197 views

Solving with DSolve recursively

I need to find $f(x,n)$ in the interval [0,1] defined by recursion, \begin{equation} \frac{d f(x,n+1)}{dx} = f(x,n) \end{equation} with boundary conditions $f(0,n+1) = 1$ and $f(x,0)=1+ x $ Using ...
7
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2answers
2k views

Finding y given x from an interpolating function

I would like to put a dot on the point of a curve that has a specific y value but I don't know the x value. A simple example of my code is ...
7
votes
1answer
271 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} ...
7
votes
2answers
616 views

How to apply restrictions to the “integrated” variable, when using NDSolve?

I have to integrate an energy along a path. I know the energy at the "beginning" of the path (energy[0]), and I can determine the energy change (gain and loss) ...
7
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1answer
139 views

Difficulty in getting correct Gaussian curve for diffusion of point source

I want to solve diffusion of a point source numerically and check it against analytical solution. first I define initial profile, ...
7
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1answer
236 views

Problem with Neumann condition in quarter disc

Bug persists through version 10.1 So I'm following the available examples in version 10 for FEM, The plane stress operator is shown as this ...
7
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1answer
162 views

Simpler code evaluating Dickman's function?

I've read here that Mathematica 10 can Obtain symbolic solutions to delay differential equations. Would that help in numericaly evaluating Dickman's function $\rho(u)$ ? It is a delay differential ...
7
votes
1answer
162 views

Wrong values at the boundary of differential equation solution

I have a second order ordinary differential equation and want to solve it numerically. Although I have specified values at the boundary, Mathematica solution does not match with boundary conditions. ...
7
votes
1answer
815 views

Extracting coefficients from a partial differential equation

Frequently, I come across the following problem: How to rewrite a complicated partial differential equation in a more clear way? I would like to create some order by collecting terms that are equal. ...
7
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1answer
231 views

mathematica 10 not showing numerical solution of differential equations?

I just got the new mathematica version 10 and tried to solve the following system of differential equation. $$r^2\frac{d^2f}{dr^2} = 2f(1-f)(1-2f)+\frac{r^2}{4}h^2(f-1)$$ ...
7
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1answer
960 views

Optimizing an energy functional in mathematica using variational calculus

I have an energy functional which I want to optimize using calculus of variation. It would be nice if someone could please post a working example using mathematica. The procedure is as follows, ...
7
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1answer
433 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) ...
7
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0answers
217 views

Partial Differential Equation in Parallel

is there any native way to implement multi-core parallel solving of PDE in Wolfram Mathematica? WM 10 now supports Finite Elements Method, but it is actually useless without parallelization. Usually ...
6
votes
2answers
478 views

Starting NDSolve from intermediate time step?

I always wondered if I could start NDSolve from an intermediate time step. What I mean is, in the code sample below, if I were to run my solution from ...
6
votes
3answers
491 views

RK4 Gravity Simulator

I have the following RK4 solver which splits the two 2nd order ODEs, used to calculate x and y positions under the influence of a gravitating body where $$x''(t)=\frac{G m ...
6
votes
2answers
747 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. ...
6
votes
2answers
264 views

Using NDSolve to produce 10,000 points of a solution

I am beginning to read the Differential Equations Laboratory Workbook by Borelli and the preface begins with an image. I understand how to use NDSolveValue (at a ...
6
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2answers
901 views

3- dimensional plot of 2-dimensional systems of differential equations

Let's take this first example of a 2D output: ...
6
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3answers
568 views

Can NDSolve handle discountinuos data?

It is possible to numerically solve a differential equation if not-smooth data are involved? For example the following instruction return the error NDSolve::bvdisc: ...
6
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2answers
2k 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 ...
6
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2answers
615 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 ...
6
votes
2answers
384 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 ...
6
votes
2answers
490 views

Symmetry-finding packages

Where can I find the most up-to-date or whatever you consider to be the most useful symmetry-finding package for differential equations? I do not intend to restrict to, but would like to include ...
6
votes
2answers
165 views

Reject diverging solution of NDSolve

I'm trying to numerically simulate a spring system with complex stiffness. In essence systems of the form $x''(t)+ (a+ ib) x(t)=0$ For this simple example an analytic solution is easy to find. The ...
6
votes
1answer
408 views

Poisson PDE over a irregular region with FDM

The problem modeled by the Poisson PDE is related to the torsion of prismatic beams and I use the Finite Differences Method (FDM). I've managed to solve the equation over a rectangle region with ...
6
votes
2answers
291 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 ...
6
votes
2answers
2k views

Is it possible to do vector calculus in Mathematica?

I am trying to rearrange and manipulate some vector differential equations in Mathematica. As far as I understand you have to tell Mathematica that a variable is a vector by specifying the components ...
6
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1answer
462 views

Using physical dimensions in Mathematica DSolve

I would like to calculate a system of two differential equations in Mathematica using DSolve, like: ...
6
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2answers
518 views

Very long Refine/Solve batch run - is my code broken, or just complicated?

So I'm trying to run some Mathematica code in batch mode from my university cluster. Specifically, I'm trying to find the equilibria of a system of ordinary differential equations. Inspired by the ...
6
votes
1answer
102 views

ParametricNDSolve[ ] and NMinimize[ ] in Combination

I have the following code that is used to simulate a spacecraft orbiting Mars, and uses ParametricNDSolve to vary the spacecraft's initial conditions using a parameter value ...
6
votes
2answers
219 views

Plotting separatrices for nonlinear system

Consider the system: \begin{align*} x'&=(1-x-y)x\\ y'&=(4-7x-3y)y \end{align*} The system has a saddle point at (1/4,3/4). How can I plot the separatrices on the phase portrait having domain ...
6
votes
2answers
211 views

RegionPlot from NDSolve

I am having quite a headache using RegionPlot to see the region of acceptance of certain coupled differential equation. I shall elaborate and try to be as ...
6
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1answer
372 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: ...
6
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1answer
246 views

How to change a parameter dynamically inside NDSolve

I have no idea how to dynamically update a parameter inside NDSolve. For example consider following first-order DE: ...
6
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1answer
180 views

Working with a system of differential equations that cannot be solved explicitly

I have to work a lot with three functions $\;o_1(t), o_2(t), o_3(t)\;$ that are solutions to the certain system of differential equations: ...
6
votes
2answers
160 views

How to use WhenEvent with a vector ODE in NDSolve

I have an ODE system I'd like to specify as a vector equation in NDSolve. I'm not clear on how to use WhenEvent for a system ...
6
votes
1answer
212 views

Solving $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$

I would like to solve the following equation: $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$ I have already posted it here, but still it doesn't work for me (I ...
6
votes
1answer
108 views

Kernel Crash while using “ValuesOnGrid” method of InterpolatingFunction

I was experiencing some kernel crash while using "ValuesOnGrid" method of an InterpolatingFunction returned by ...
6
votes
1answer
677 views

Modelling a Rocket Launch using NDSolve

I'm trying to model a rocket launch with Mathematica but I've run into a little problem since I don't know how to turn the thrust off. I'm using Newton's Law of Universal Gravitation plus an added ...
6
votes
1answer
140 views

Long running ToElementMesh with very “large” domains

I'm trying to solve a system of PDE over a large domain. This doesn't means I need to have a huge amount of mesh points and mesh elements to discretize the domain. Just that the domains has a big ...
6
votes
1answer
347 views

Changing a wave simulation

I want to adjust some code that I found on this Wolfram Demonstration: http://demonstrations.wolfram.com/WaterRipplesPassingThroughASlit/ Basically it shows a wave passing through a single slit. I ...
6
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1answer
1k views

How do I find the best parameter to fit my data if the model is a interpolating function?

Hi I have a question regarding to find the best parameters for my model to fit my data. I have 3 ordinary equation, and I now just picked some parameters (...