MaplePrimes - Questions and Posts tagged with ode

Differentia Equations Mixing Problem

BeeMariex3 — Fri, 10 May 2013 21:02:48 Z

Hi, I have a maple project and one of the questions reads:

a. | Initially, a 100 liter tank contains a salt solution with concentration 0.5 kg/liter. A fresher solution with concentration 0.1 kg/liter flows into the tank at the rate of 4 liter/min. The contents of the tank are kept well stirred, and the mixture flows out at the same rate it flows in.
i. Find the amount of salt in the tank as a function of time.

ii. Determine the concentration of salt in the tank at any time.

Plotting a three dimensional phase plane

P_Sampras — Mon, 06 May 2013 14:49:42 Z

Below is my code for solving a solution of three first order ODEs using the 4th-order Runge-Kutta method.

I have been able to successfully plot the solutions of each of the ODEs (x,y,z) against time t, however I am struggling to produce a plot in the three dimensional phase domain of x,y,z. Could anybody suggest what commands to use as everything I have tried (plot, plot3d, implicitplot3d etc) has produced an error.

h:= 0.01:
N:= 200:
x:=Vector(N+1):

The damped driven pendulum

tommytin — Thu, 28 Mar 2013 07:52:40 Z

The damped driven pendulum is modeled using :

d²(x)/d(t²) + b*d(x)/d(t) + sin(x) = F*cos(x). (4)

Numerically simulate (4) with b=0.22 and F=2.7

a) Starting from any reasonable initial condition, perform a phase portrait analysis. Show that the time series has an erratic appearance, and interpret it in terms of the pendulum's motion.

b) Plot the Poincare section by sampling the system whenever t=2*pi*k, where k is an integer.

How to compare or perform phase portrait ( diff(theta(t) vs. theta)?

tommytin — Thu, 28 Mar 2013 07:35:15 Z

d^2(x)/d(t^2) + sin(x)=0 (1)

d^2(x)/d(t^2) + x = 0 (2)

d^2(x)/d(t^2) + ( x - (x)^3/6) = 0 (3)

1) Compare the results of numerical simulations of (1), (2), (3) to see how closely the period of the periodic orbits relate.

a) Perform a phase portrait ( (x)'(t) vs. x ) analysis for (1), (2), and (3).

b) Consider the initial conditions x(0)= x₀ and x'(0)=0. For what intervals of x₀do the periodic orbits of (2...

plot solution of ode with max and min

reemeaaaah — Tue, 19 Mar 2013 04:57:06 Z

Hello

I am trying to plot solution of ode0 together with the maximum and minimum values but I am having difficulty since the first plot is a solution and second is values. I should have a plot with two line one represent the solution of ode0 and second (the max an min). Any advise or suggestion?

This is the code:

> restart;
with(DEtools); with(plots); Nsols := 5; Ntstep := 10;
k := 0; A := 0.37e-1; B := 0.2e-6;
ode0 := diff(U(t), t) = -(A+B*U(t))*U(t);

recursive assignment

zyjfeelsgood — Tue, 12 Mar 2013 23:20:11 Z

part of my codes are:

func[1] := (1/2)*(c+s)*x[1]+s*x[3]+(s-c)*x[1]*x[2];
func[2] := (1/2)*(c-s)*x[1]+s*x[3]+(s+c)*x[1]*x[2];
func[3] := -b*x[2]-x[1]^2;

They are just three ODE , how to fix the error?Where is the so-called recursive assignment...?

The program works well when:

"func[1] := x[2] + (x[1]^2 - x[1]*x[3]);

func[2] := - x[1] +  (x[2]^2 + x[1]*x[4]) + x[2]^3;

Inexplicable Error while solving for Steady State Solutions

Maturo — Fri, 22 Feb 2013 21:09:34 Z

I was trying to solve for the equilibrium points for a system of differential equations. Solving for the last equation, I encountered an error that I can't seem to find anywhere else. "Error, (in Engine:-Dispatch) not implemented yet: 13". The code is below if anyone wants to take a go a figuring what's up. Thanks!

A:=Asource/muA;
                            Asource
                            -------
                              muA

shaded area in plot and 95% confidence intervals

reemeaaaah — Wed, 20 Feb 2013 17:20:20 Z

Hello,

I am trying to get a shaded area in my plot but I could not.

First we solve ODE without randomness:

ode := diff(U(t), t) = -(A+B*U(t))*U(t);

Then we add randomness to ODE and solve:

ode2 := diff(U(t), t) = -(A+r(t)+B*U(t))*U(t);

A with randomness for r in R=( - 0.0001/365, 0.0001/365) is:

A(t,r)= A+r

Where A is constant = 0.0001/365

We plot both solution. For the plot I...

Failing to integrate a ODE

sakhan — Tue, 19 Feb 2013 16:40:03 Z

Hi all I have the following ODE

ODE_1:=diff(w(r),r)+R*(diff(w(r), r))^3=K/r;

ODE_T_1:=collect(algsubs(w(r)=u(r)+(r-1)*(U-0)/(delta-1), ODE_1),diff(u(r), r)) ;

and when I try to do the following integration,

eq1:=int(phi[i](r)*ODE_T_1,r=1..delta) assuming delta > 1;

it gives the following error

Error, (in assuming) when calling 'int'. Received: 'wrong number (or type) of arguments:

How do I analyse a numerical solution to a system of ODEs?

di2g10 — Sun, 17 Feb 2013 15:00:01 Z

The system of ODEs i am trying to analyse is just a 3d model of a ball in motion with gravity and air resistence acting upon it.

restart;

with(plots):

eq1 := diff(x(t), t, t) = -k*sqrt((diff(x(t), t))^2+(diff(y(t), t))^2+(diff(z(t), t))^2)^(n-1)*(diff(x(t), t))

eq2 := diff(y(t), t, t) = k*sqrt((diff(x(t), t))^2+(diff(y(t), t))^2+(diff(z(t), t))^2)^(n-1)*(diff(y(t), t))

eq3 := diff(z(t), t, t) = -g-k*sqrt((diff(x(t), t))^2+(diff(y(t), t...

Two Separate Procedures - Plotting on the same graph.

Hopkins — Fri, 08 Feb 2013 15:14:17 Z

Hi,

I have two separate procedures, one which solves a series of ODE's using the midpoint runge-kutta method, and one which solves using the Taylor expansion.

I am able to graph the two results (Q1 vs time) on separate graphs within the procedure, however after "end proc" I can't retrieve the figure or plot the two seperate results on the same graph to compare the values.

Is there an easy way of doing this or do I have to rewrite the procedure to include both methods?

Solution Curve in Maple 16

stefancw — Thu, 24 Jan 2013 01:45:35 Z

Hi, I am trying to plot a solution curve on a vector field with an initial condition of y(0)=0 and I keep getting error messages. This is what I have so far:

with(DEtools); dfieldplot(diff(y(x), x) = x^2+y(x)^2-1, y(x), x = 0 .. 5, y = -1 .. 5, arrows = line, title = 'Slope*Field');

Thank you.

Problems with DEplot

ncorbett — Sat, 19 Jan 2013 22:23:03 Z

Hi,

After upgrading to Maple 16.02, the Maple code:

eqn3:=diff(y(x),x)=x+sin(y(x));
IC3:=[y(0)=2,y(3)=0];
DEplot(eqn3,[y(x)],x=-5..5,IC3,y=-5..5,arrows=comet,linecolor=BLACK);

produces the directions field but fails to produce the solution curves.

I have tried the same code on two different machines running Maple 16.02 with identical results. I have also tried the code on Maple 16.01. In this case the solution curves are produced.

How do i substitute the values of my solved ode functions in a separate equation

JpK1meet — Wed, 09 Jan 2013 06:56:07 Z

I have already solved my ODEs and used odeplot to analyse the change over time (0 to 10).

Below is my ODE,

d(a(t))/dt = x - y*(a(t))

d(b(t))/dt = m*a - n*(b(t))

My query here is,

I need to substitute a(t) and b(t) in a seperate equation,

h(t) = 60/0.98 * (a(t))*(b(t))

and i need to plot 'h' over time (0 to 10)

How do I go about doing this?

Please help.

Thanks.

Correlation coefficient for system of nonlinear differential equations and data

kierstejn — Wed, 12 Dec 2012 19:35:44 Z

Hey guys..

I need some help on determining the correlation coefficient between my data points for an Influenza epidemic and the SIR model, with my estimated parameters Beta and Alpha. The initial conditions for the equations are defined at the beginning of my worksheet:

SIR_model.mw

Hope someone can help me ;)