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Is it possible to describe billiards in the unit square (see for info) in terms of events and if? For example, let the dynamical system
{x''(t)=0,y''(t)=0, x(0)=0.5, x'(0)=0.2, y(0)=0.5, y'(0)= sqrt(3)/5}
be given, where the trajectory [x(t), y(t)] satisfies the usual laws of reflection when reaching the boundary {x=0}, {x=1}, {y=0}, {y=1}. The same question about billiards in the unit disk.

10 000 000...

January 13 2014 Valery Cyboulko 120 Maple


January 2014: Pages of oldest Russian Maple Application Center have been opened 10000000 times.


I  have a system of second order differential equation to be solved numerically. I would like to set up events to halt integration  to find the values of phi when r(phi)=2/3 . Here is my code




The code only works for the second event so it halts for r(phi)=1.63... etc

How do i stop this?


Thanks for any help.

My problem is How to use events command in dsolve/numeric for different points of independent variable?                                     A simple example:


ds:=dsolve({de,x(0)=1}, numeric, method = rkf45,abserr=1E-12,relerr=1E-11,events =[[x(t)-1E-8,halt]]);

works perfectly, but I need to compare x(t) and x(t-h) in two consecutive...

HI,is it possible to solve the ODE system (that I have uploaded) by adding events at a certain timestep, instead of reformulating the system for each step.The ODE system expresses two coupled movements y(t) and X(t). The current position of y(t) is controlled by a parameter which depends on values calculated in the previous step, while changing the sign for each step.Thank you! 


     So I've got a numerical solution to a D.E. and want to find which parameters (v, theta) cause the second event to occur. Here's my dsolve

> soln:= dsolve({eqx, eqy, inty, intx, x(0)=0, y(0)=0}, {x(t), y(t)}, numeric, method = rkf45, output=listprocedure, parameters=[v, theta], events=[ [ [diff(y(t),t)=0, y(t)

 The first event is "Does the trajectory reach its max at a height less than 3.05m? If so, stop computation"...


I have the same problem.

   "Simulation problem: maximum number of event iterations reached (100) at t= ...."

I have a model which worked without problem in maplesim2, using a lot of event iterations. The model can only work this way, becouse its a mechanic model where the friction is function of the sliding speed, thus where the speed changes value, the friction coefficient does also, and an event occurs.

I really need to know where...

What is meant by events? I have seen this error numerous times.

   "Simulation problem: maximum number of event iterations reached (100) at t= ...."

How do I model so that I can avoid them?

My question is related to this discussion on "querying events"

I thought I might start a new thread.

The following loop is an illustration of the sort of thing I'd like to do with dsolve and events: I loop over a parameter of the "event" and extract information on the solution at different values of the parameter. Here is the code (successfully tested on Maple 15 / Standard / Windows)...

I have a system of 3 ODEs in 3 variables x(t),y(t),z(t) to be solved numerically. I would like to set up events to halt integration as soon as one of the derivatives changes sign.

I've tried things like:

'events' = [ [ diff(x(t),t) >0, 'halt'] ] :

'events' = [ [ diff(x(t),t) = 0 .. 0.1, 'halt'] ] :

I might have tried something like increasing(x(t)) (how nice and intuitive), but if I understand correctly the help page on this, increasing(x(t)...

And so with this provocative title, "pushing dsolve to its limits" I want to share some difficulties I've been having in doing just that. I'm looking at a dynamic system of 3 ODEs. The system has a continuum of stationary points along a line. For each point on the line, there exist a stable (center) manifold, also a line, such that the point may be approached from both directions. However, simulating the converging trajectory has proven difficult.

I have simulated as...

dsolve event handling looks like a great tool, but I can't understand how it works and it's not sufficiently popular to google my way to examples online. There are two things I'd like to do: 1) interrupt the computation once some variable leaves a certain range, 2) interrupt the computation if the solver gets stuck into an infinite loop. Both are documented in the help, but I don't understand it. Suggestions welcome, thanks!


I made an upgrade from Maple 13 to 14, but a program i wrote with maple 13 (ode event handling) simply is incorrect in maple 14. The events aren't recognized anymore. What is the problem?

Thank You.


I i have a 2nd order ODE where i want to chance the derivatives of x(t) and y(t) exactly at sqrt(x(t)^2+y(t)^2)=1 ,or before, as close to 1 as possible.

I found "event=" in/dsolve/numeric/events, where i can define the trigger and the action.

What is the difference between: "event=[[sqrt(...)-1,diff(x(t),t)=...],[sqrt(...)-1,diff(y(t),t)=...]]" and "event=[[sqrt(...)-1,[diff(x(t),t)=...,diff(y(t),t)=...]]]", because i get different results, which one is the correct form?

Raptor Math...

August 05 2010 Dave L 467 Maple

This describes in more detail (with permission and citation) the method posted here of solving problem 2 in the XKCD comic Substitute.




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