I am fitting polynomial differential equations to data, and I came across some troubling behavior. I have sets of coordinates in x, y, z, and values w at these coordinates. The x,y,z coordinates and the data at these coordinates are concatenations of three subsets of data each, and depending on the order of the concatenation, I get different polynomials from the stats fit command. The difference is not trivial -- it makes a huge differentce in the stability of the differential equations. I have written a demonstration worksheet to show this problem.

John Starrett

Solve IVP with complex coef. with compplex varables numerically..

the sys. is x'=-iDelta1x(t)+y(t)+epsilon

y'=-iDelta2y(t)+x(t)z(t)

z'=-2(x*(t)y(t)+x(t)y*(t)), where * means complex conjugate 

I solve it as:

epsilon:=5:Delta1:=4:Delta2:=4:assume(z(t),real):

var:={x_R(t),y_R(t),z_R(t),x_I(t),y_I(t),z_I(t)}:
dsys :={diff(x(t),t)=-I*Delta1*x(t)+y(t)+epsilon, diff(y(t),t)=-I*Delta2*y(t)+x(t)*z(t), diff(z(t),t)=-2*(conjugate(x(t))*y(t)+conjugate(y(t))*x(t))}:
functions := indets(dsys, anyfunc(identical(t))):
redefinitions := map(f -> f = cat(op(0, f), _R)(t) + I*cat(op(0,f), _I)(t), functions):
newsys := map(evalc @ Re, redefinitions) union map(evalc @ Im, redefinitions):

incs := {x_R(0)=0, x_I(0)=0, y_R(0)=0, y_I(0)=0,z_R(0)=-1/2, z_I(0)=0}:
dsol1 :=dsolve({newsys,incs},var,numeric, output=listprocedure, abserr=1e-9, relerr=1e-8,range=0..1):

but it seems there is not runing propebly

If we a complex number in Maple, like for example:

I*b+a+x+I*y+I^2*c

How can we make maple rewrite it like this?

a+x-c+I*(y+b)

I tried using the comands Re(%) and Im(%) but Re just gives the whole expression again and Im gives 0.

Hey

I have a excel spreadsheet with a number of data points which I want to plot in Maple.  I have imported the data and I did manage to produce a point plot, but how can I exclude some of the data points when I plot the point plot?
I would, for example, like to exclude the negative values and only plot the data which is greater than zero.

Thanks

I am relatively inexperienced with Maple and would like to either be pointed in the right direction or shown a similar example to my problem for reference.

My problem is I need to write a programme using the below equations

d^2x/dt^2=ax+by

d^2y/dt^2=cx+by

I then have to use the below values to show my programme works

a=b=c=d=1

x(0)=1

Dx(0)=0

y(0)=0

Dy(0)=1

After proving it works I have to apply it to a mass spring system using realistic parameters. Using visual and analytical ways to show findings.

md^2x/dt^2=-kx-k(x-y)

md^2y/dt^2=-k(y-x)-ky

when x and y are the displacement from the equilibrium. Initially the masses are displaced from their equilibrium posistions and released so that

x(0)=a, y(0)=b, Dy(0)=Dx(0)=0

then repeat with different smaller calculations

Any help would be much appreciated

Thanks

When I write in maple the following:

x*(x+y)

What do I need to write to make maple make the operation that will evaluate the expression and show the following?

x^2+x*y

simplify(%) or evaluate(%) only shows it the same way it was inputted to start with.

Hi,

  I have the following code for using "PolynomialSystem" solve equations of polynomial

*********

with(SolveTools):

f:=PolynomialSystem({x+y-3, x^2+y^2-5}, {x, y}):

print(x,y);
print(f);
f[1];f[2];
a:=f[1][1];b:=f[1][2];
print(a,b);
c:=-evalf(a);d:=-evalf(b);

****************

The output is

***

x, y
{x = 2, y = 1}, {x = 1, y = 2}
{x = 2, y = 1}
{x = 1, y = 2}
x = 2
y = 1
x = 2, y = 1
-x = -2.
-y = -1.

***

From what I have seen, I cannot subtract the values of x and y as 2 and 1. Is there any way that I can get the values of solutions of variables, namely I can assign a variable "a" as 2, and the other variable "b" as 1?

Thank you very much!

How can one deduce values of f(eta), diff(f(eta),eta) and diff(f(eta),eta$2) from values of f1,f2,f3,f4,.. in the results of the finite difference here Trial.mw . I need the outcome for f and its 1st and 2nd derivatives as listed above. Please help.

How do I compute the Lyapunov exponents for Lorenz system

Is it possible to organize output of plots in Mathematica-like manner

in one list (placed in one cell)?

In Maple I use tables for these purposes:

Maybe, does there exist a more elegant solution?

hi...plese help me

:

how i can solve set of non linear differential equation with a unknown parameter with numeric role in maple software??

thank a lot ...

Hello, my problem is that I've changed in tools maple default mode to "Maple input" from "2-d" I've aplied it globbaly and it doesnt'work. Still when type Enter it switch automatically to 2-d Math, and I have to change it by Ctrl-M to 1-d. Any ideas how to solve it? I want 2-d just to output.

I want to solve the equations eqn3 and eqn4 to solve the  tan(alpha)  and tan(beta),  give me a help .thanks a lot 

Download 0112.mw

I just started my Calculus I class and I have a project to prove some various theorems. Maple rocks for this. 

How can I insert the Q.E.D. symbol (looks like a little black square) at the end of my proofs?

ok so I run Maple 18 , but the problem is that maple does not show me the phase portrait , it only keep showing me what i write,

for example , i write this  

  DE1 := diff(y(t),t) = z(t);
  DE2 := diff(z(t),t) = -y(t)*cos(t);
  phaseportrait([DE1,DE2],[y,z],t=-5..5,[[y(0)=1,z(0)=0],[y(0)=0,z(0)=2],[y(0)=0,z(0)=-2]],y=-Pi..Pi,z=-3..3,color=aquamarine,linecolor=blue);
  
and maple just show me these back 
what should i do?