Maple 2015 Questions and Posts

These are Posts and Questions associated with the product, Maple 2015

Hi there,

I have an ode that I want to plot, I am trying to plot 2 different graphs on one graph and have tried using display but cannot seem to add a legend to it. Someone suggested adding a legend to each individual graph before combining them but I cannot find out how to add a legend to a DEplot. My code is as follows:

 

ode:=diff(u(t),t$2)-0.1*(1-64*u(t)^2)*diff(u(t),t$1)+16*u(t)=0

Q1:=v/4*sin(4*t)+epsilon*(1/8*(v-v^3)*t*sin(4*t)+v^3/128*(cos(4*t)-cos(12*t)))

A:=DEplot(ode,u(t),t=0..10, [[u(0)=0, D(u)(0)=v]], u=-0.5..0.5, linecolor=black, linestyle=dash, title="Numerical Solution"):

B:=plot(Q1, t=0..10, u=-0.5..0.5,color=blue, legend="Regular Perturbation Expansion"):

display([A,B],title="Comparing the regular perturbation expansion to the numerical solution")

 

Many thanks

Good day everyone,

I'm relatively new to Maple, and I study engineering (not maths), so maybe my problem is related to a bad approach of the equations.

The problem is that I'm asking Maple to do a double integral of a "complex" expression and it only solve the first integral, but not the second.

Here is the code:

https://www.dropbox.com/home/C%C3%81LCULO%20FUERZAS

Thanks.

Dears!

Hope everyone should be fine. I am face to import excel sheet in maple. I saved execl sheet with name "Employees.xlsx" at desktop. When I use the following command
S := Import("Employees.xlsx", 1, "A1:B101");

I got the following error. 

"Error, (in ExcelTools:-Import) Could not open the file"

Please help me to fix this problem. I am waiting positive response. 

Special request to:

@Carl Love
@Preben Alsholm
@acer

Hi everybody,

I use dsolve(..., numeric, events =[...], parameters = [...], range=0..TMAX) to solve a parameterized system of 2 ODEs (unknowns x(t) and v(t)).

The solution over the whole range [0, TMAX] is constructed by assembling partial solutions over adjacent subranges of [0, TMAX].

(please look the attached file and feel free to contact me if you need more details than those given below

There exist two types of solution :

  • Type 1 : trivial solution : for all t in some range [a>=0, b<= TMAX], the solution is x(t)=0 and v(t)=0
  • Type 2 : for all t in some range [b>=0, c<= TMAX] {x(t), v(t)} is the solution of the differential system


The end of the simulation corresponds :

  • either to t=TMAX
  • either to x(t) = CMAX where CMAX is some predefined value for x(t)
     

I use events to manage the two following situations 

  • x(t) = CMAX
  • x(t) = 0 and v(t) < 0 : this is the situation which describes the transition between Type 2 solutution and Type 1 solution


The global solution is constructed by assembling partial solutions over subranges [0, b[1]], [b[1], b[2]], [b[2], b[3]] ... where type 1 solutions "live" in [b[n], b[n+1]] if n is odd and type 2 solutions in  [b[n], b[n+1]] if  n is even.
 
The assembly of the partial solutions doesn't work correctly : I identified the reason but I'm not capable to fix it.
If you look to the red instructions on yellow background you will see they do not return the same answer than the pink instructions (look to the blue outputs over the plot) . 

This is probably due to a very big mistake on my part  but I can't fix it !

Once again, if my explanations are not sufficient or if I'm not enough clear, feel free to ask me any questions you need.

Thanks in advance

 

ParametricDsolve.mw

 



 

I wanted to calculate the bessel function's limit, but there is no results.


 

NULLNULLwith(MTM):

constants := s

s

(1)

eq1 := `assuming`([limit(MTM:-bessely(1, -I*r*sqrt(s)), infinity)], [s > 0])

BesselY(1, -(infinity*I)*s^(1/2))

(2)

eq2 := eval(eq1)

BesselY(1, -(infinity*I)*s^(1/2))

(3)

eq3 := `assuming`([limit(MTM:-bessely(1, -I*r), infinity)], [s > 0])

BesselY(1, -infinity*I)

(4)

eq4 := eval(eq3)

BesselY(1, -infinity*I)

(5)

eq5 := `assuming`([limit(beselj(1, -I*r*sqrt(s)), infinity)], [s > 0])

beselj(1, -(infinity*I)*s^(1/2))

(6)

eq6 := eval(eq5)

beselj(1, -(infinity*I)*s^(1/2))

(7)

eq7 := `assuming`([limit(MTM:-besselj(1, -I*r), infinity)], [s > 0])

-I*BesselI(1, infinity)

(8)

``

``


 

Download test.mw

The initial conditions are U[13.75]=0.7787 and U'[13.75]=0.344037

Dear users! I need the help in attached file. Please see and fix it. I am waiting your positive answer.

File_to_help.mw

Hi everybody,

I use the Grid package to do intensive computations.

For some reason I'm ignorant about, the test case described in the Grid[Server][StartServer] 

 help page doesn't work with Maple 2015 (neither on Mac OS X, neither on Windows 7 ; here is the mw file run on MAC Os X)

Could someone explain me why (probably something I did not read with enough attention ... some license maybe) ?
Thanks in advance

GridServer.mw

Hello
I try to reproduce in Maple this document in pdf. In it you can see the code in MathCad to find the roots of a system of equations by the method of Draghilev.
After seeing some of the codes posted in the Maple forum where the development of the method is shown and reading the document in the Application Center, some questions arise.
When the deferential ecacuion system is divided, in this case stored in variale b [i], by b [i] / (b [1] ^ 2 + b [2] ^ 2) ^ 0.5; i = 1..n + 1
Why, as I could see in some systems, the first two differential equations are taken and in others it takes three?
And in what systems does it divide at all?

https://www.mapleprimes.com/view.aspx?sf=223821_question/Draghilev

 

In this case in my transfer of code from Mathcad to Maple I do not get the initial values of the system fsolve calculates indefinitely

sistema9.mw

 

Hello,

I'm trying to evaluate an integral (code snippet and screen-shot included below) assuming that certain parameters and integers. Using assume statements the integral evaluates to 0. However, if I evaluate the integral for a specific set of integers, the integral evaluates as non-zero.

Can anyone clarify why the two int statements return different values?

Thanks!

assume(K::integer);
assume(L::integer);
assume(M::integer);
int(sin(K*x)*sin(L*x)*cos(M*x), x = 0 .. Pi);
     returns: 0
int(sin(14*x)*sin(2*x)*cos(12*x), x = 0 .. Pi);
     returns: Pi/4

How do you way text below

Maple 2015 

if i use function cat() is not 

 

The attached worksheet performs two functions:

(1) It lets me print 4 × 6 Index Cards for the short entries in each table.

(2) It allows for easy storage and retrieval of syntax (code).

The worksheet has many tables, each separated by a Page Break.

Questions:

(a) Is there a way to sort all the different tables so they will be arranged in alphebetical order?

(b) When I select one table to print and open the Print Dialog, the "Selection" option is grayed out. (see graphic below).  (1) Is there a way to enable the selection option?  (2) Is there a way to determine what page I am on so I can use the "Pages from...to" option?  If I need to number the pages, will the page numbers reset to parallel a new alphabetic sort order.

Many thanks in advance.  See WC29_4_BY_6_NOTE_CARDS_UNSORTED.mw attached. And see image of Print Dialog below.

Les

Dears 

Hope you all are fine. I want to solve the following nonlinear system ODEs numerically

Eq1 := diff(F(eta), eta, eta, eta)-phi1*((diff(F(eta), eta))^2-(diff(F(eta), eta)+diff(G(eta), eta))*(diff(F(eta), eta, eta)))+alpha*(1-phi)^2.5*((diff(F(eta), eta, eta))^2+2*(diff(F(eta), eta))*(diff(F(eta), eta, eta))-(diff(F(eta), eta)+diff(G(eta), eta))*(diff(F(eta), eta, eta, eta, eta))+A*(2*(diff(F(eta), eta, eta, eta))+(1/2)*eta*(diff(F(eta), eta, eta, eta, eta))))-A*phi1*(diff(F(eta), eta)+(1/2)*eta*(diff(F(eta), eta, eta))) = 0; Eq2 := diff(G(eta), eta, eta, eta)-phi1*((diff(G(eta), eta))^2-(diff(F(eta), eta)+diff(G(eta), eta))*(diff(G(eta), eta, eta)))+alpha*(1-phi)^2.5*((diff(G(eta), eta, eta))^2+2*(diff(G(eta), eta))*(diff(G(eta), eta, eta))-(diff(F(eta), eta)+diff(G(eta), eta))*(diff(G(eta), eta, eta, eta, eta))+A*(2*(diff(G(eta), eta, eta, eta))+(1/2)*eta*(diff(G(eta), eta, eta, eta, eta))))-A*phi1*(diff(F(eta), eta)+(1/2)*eta*(diff(F(eta), eta, eta))) = 0;

assoicated with the following BCs

F(0)=0,D(F)(0)=1,G(0)=0,D(G)(0)=p, D(F)(L)=0, D( G(L)=0;

for phi1 := 1.2; alpha := 2; A := 1.5;phi:=0.1;

Please help me to find the solution

Special request to @acer@Carl Love @Preben Alsholm

can result ?

Please help me?

Hi,

I am a little bit surprised by the result of the operation evalf[8](f(y)) in the piece of code that follows.
I was expected the answer to be 2.4494897, not 2.4494898.

Happily the sequence
res := f(y) ; evalf[8](res)
returns the expected result 2.4494897

I suspect the difference comes from some precedence of the operators (f and evalf) but I can't figure out what really happens

Could you enlight me please ?

Thanks in advance

 

restart:

interface(version);

`Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895`

(1)

Digits;

10

(2)

f := x -> sqrt(2.0)*x;

proc (x) options operator, arrow; sqrt(2.0)*x end proc

(3)

y := sqrt(3.0):

f(y);

2.449489743

(4)

evalf[9](f(y));  # right

2.44948974

(5)

evalf[8](f(y));  # ????

2.4494898

(6)

res := f(y);
evalf[8](res);  # right

2.449489743

 

2.4494897

(7)

 

 

 

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