Hi all,

I am trying to solve the following differential equation numerically using dsolve,

y * abs (y''') = -1

y(0) =1, y'(0) = 0, y''(0)=0

it works fine when tthe absolute function is not there, i.e. yy''' = -1. 

Do you have any suggestion?

I have solved ODE's with either i.c. or b.c. (mechanics stuff) where the results were in terms of expressions, not functions.  I could plot these expressions, substitute values in for parameters, etc. 

Then I thought that the real way to solve an ODE or system of ODE's was to define functions.  I wanted this to be in three levels: the solutions in generality, the solutions with i.c./m.c. applied, and then further with the parameter values defined. 

So far, no joy.  Lots of confusion--input eqns as sequence, list, set?  I looked on the Maple help page, thought I was doing things right. I even tried out "union" for the ode's and the ic's.

The code is below; statement (11) produces an error. Yes, I am using Maple 18, even though the file says Maple 15.  I'd like to solve the 4-ODE system at the three levels listed above, and then (if possible), plot the result! Am I asking too much?  Should I be using MapleSim or some other product instead?

Thanks for any and all help!

robert w.

Download mae340_state_space_4-ode_system.mw

how to shift shift(1,[x,y,z]) = [y,z,x]

shift(2,[x,y,z]) = [z,x,y]

shift(3,[x,y,z]) = [x,y,z]

Hello Maple


I am preparing for an examination in Calculus, but my worksheet in Maple 18 doesn't cooperate. 

A lot of my studypartners use Maple 16 and they have no problems. 


I meet the following error: 

- Error, (in solve) invalid input: hastype expects 2 arguments, but received 1


I'm totally sure, that I'm typing correctly, because I write just the same as my studypartners. 
So is it an error, which only is seen in Maple 18 and can I do anything to solve the problem?

Kind regards
Anders Kristensen

PS: I can't figure out how to add a picture

I solve the problem on computational geometry: "A cube of side one contains two cubes of sides a and b having non-overlapping interiors. How to prove the inequality a+b≤1?" To this end I use the DirectSearch package , namely,

Here are some comments to it. The cube of side a is centered at (x_1,y_1,z_1) and rotated by the angles phi_1, psi_1, theta_1 (see http://uk.wikipedia.org/wiki/%D0%95%D0%B9%D0%BB%D0%B5%D1%80%D0%BE%D0%B2%D1%96_%D0%BA%D1%83%D1%82%D0%B8 ) and the cube of side b is centered at (x_2,y_2,z_2) and rotated by the angles phi_2, psi_2, theta_2. The procedure

calculates the distance between these cubes, for example,

st := time(); dist(.2, .9, .2, .2, .2, .7, .7, .7, 0, 0, 0, 0, 0, 0); time()-st;

[HFloat(5.453016092898238e-11), [s1 = HFloat(0.2646161775314957),

  s2 = HFloat(0.2828503247068887),

  s3 = HFloat(0.29444713116943216),

  t1 = HFloat(0.2646161774916062),

  t2 = HFloat(0.28285032471998384),

  t3 = HFloat(0.2944471311346344)], 2527]
                            191.133
Unfortunately, my code (which is syntactically correct) is spinning on my wondercomp during 10 hours without any output. I don't understand it at all. Your advices are welcome.

twocubes.mw

Hi there,

I have an ODE system which apparently needs some initial conditions to have its vector field plotted.

I am giving Maple's dfieldplot function the following arguments:

dfieldplot([de1, de2], [A(t), G(t)], t = 0..1, [A(0) = 25, G(0) = 0], A = 0..900, G = 0..200)

But Maple yields an error that reads:

Error, (in DEtools%2Fdfieldplot) invalid use of initial points or option - see phaseportrait

I would say that the initial conditions are correctly stated, according to the documentation of the function.

This is the attempt: MaplePrimes_Malaria_infection_cont.mw

Any ideas on what's missing?

Thanks,

jon

Hi there,

I would like to have the Jacobian matrix of an ODE system evaluated, and their eigenvalues computed, at the steady states of the system.

I know how to get the Jacobian matrix evaluated and the eigenvalues computed on an individual basis, setting manually each steady state as the argument of the matrix.

However, I would like to have it in a loop, so that the loop manages all steady states, that is:

steadyStates:= solve(mySystem); # would yield a set of pairs/lists

for each steadyState

m:=Jacobian(steadyStateN); # evaluate the Jacobian matrix

ev:= eigenvals(m); # compute the eigenvalues and save them to another variable/array and print them

end for:

First, I am not to find a way to loop over my steadyStates.

Attached is an example where the Jacobian matrix and eigenvalues are computed individually, where the steady states have been hard-coded once they have been computed: MaplePrimes_Predator_prey_model_Jacobian.mw

Any ideas on how to do this?

Thanks,

jon

Hi there,

I would like to compute and display the nullclines of a set of ordinary differential equations.

AFAIK, I can compute the nullclines in Maple by defining the equations and solving the system

e.g.:

# Define the equations
eq1 := u(t)*(1-u(t)/kappa)-u(t)*v(t) = 0;
eq2 := g*(u(t)-1)*v(t) = 0;

# Solve the system (i.e. compute the nullclines)
sol := solve({eq1, eq2}, {u(t), v(t)});

However, I am not quite able to imagine how to display them over a dfieldplot or a phaseportrait.

Attached is an example with some differential equations, and their vector field and trajectories: MaplePrimes_Predator_prey_model_nullclines.mw.

It can be use to illustrate how to (compute and) display the nullclines.

Thank you,

jon

Hi there,

I would like to have an operator (in this case, the natural logarithm) applied to a list/array of points defined as:

ydata := [0.572594976618e-1, 0.327865007249e-1, 0.280821589546e-1, 0.114365745192e-1, 0.578537931608e-2, 0.139154661062e-2, 0.641467839994e-3, 0.18013801847e-3];

How can I apply Maple's ln() operator to the whole array (i.e. avoid to apply it to ydata [1], ydata [2], etc.)?

Thank you,

jon

Aslam-u-Alikum. Hope you will be fine. I facing the problem of the last line to the attached program. I need the values of lambda in decimal.

Help.mw

PhD (Scholar)
Department of Mathematics

Hi,

I am trying to solve following expression

int(int((1-exp(-5.5/cos(x)))*sin(x), x = 0 .. arctan(300*cos(y)+sqrt(12.25-90000*sin(y)^2))), y = 0 .. Pi)

But I am not getting results.

Please help me!!!

Thanks

Cannot calculate derivative (gradient) of a procedure returned by dsolve.

Say, I solve the equation:

S1 := dsolve([diff(y(x), x$2)-1.0325*diff(y(x), x)+1.36*y(x)=sin(2*x), y(0)=0, y(1)=1], numeric, y(x), 'output' = listprocedure);

Its solution easily can be retrieved and looks fine:

H:=rhs(S1[2]); 

plot(H(t), t = 0..1, thickness = 4);

But when I try to calculate the gradient of H, I receive the error:

H1 := codegen[GRADIENT](H);

Error, (in intrep/statement) unable to translate Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(8, {(1) = .0, (2) = .14817993189456188, (3) = .31785812820433257, (4) = .47163479035679234, (5) = .6130306894371967, (6) = .7460958115245858, (7) = .8741894219027533, (8) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(8, 2, {(1, 1) = .0, (1, 2) = .47692145669848085, (2, 1) = 0.7710429970702501e-1, (2, 2) = .5707930170882397, (3, 1) = .1866916935738028, (3, 2) = .7299040171277492, (4, 1) = .3128649714509215, (4, 2) = .9171936...

Gradient of procedures defined by  ":= proc()" is calculated properly.

When you label a function of curve, this label is put just next to it. Is there a way to move this label to another position of the same curve?

Hello friends!

I 'm a student and I don't know a lot about Maple, so I would be really grateful if anyone could help me.

I want to solve a system of two equations and I have two unknowns, which are k and εα. However I don't know what I am doing wrong and I can't solve it.

I have attached my file.

Thank you very much in advance!agogos_2.mw

I am trying to fit an experimental data C[A](t)  vs t, with modelled ODE equation by solving it with numerical method. But the process gives problems here ha code and also find attached maple file.

Input is time =[0, 30, 60, 90, 120, 150, 180, 210, 240]

and output exptal data = [7647.5, 7397.5, 6755, 6252.5, 5860, 5530, 5440, 5107.5, 4857.5]

I want to find k,K[A] parameters;

EXPT_datafittinh_LHHW.mw