Maple 2019 Questions and Posts

These are Posts and Questions associated with the product, Maple 2019

I need the Infinitesimals(Lie group analysis) of the system of PDE. I have attached below the system of PDE in MAPLE given below.MAPLE_Help.mw

Thank you

Hello,

I am trying to solve the following system of odes where the unknowns are xhat, yhat, uhat and vhat. They depend on the variables (x, y, u, v, a_1, a_2, a_3, a_4, f(x)) where f(x) is an arbitrary function and I want to solve it with respect to a_1. The RHS has f(x) and its derivative with respect to x. The dsolve function fails to solve the ode when I add f(x) at the list of variables. 

restart;
vars := x, y, u, v, a_1, a_2, a_3, a_4, f(x);
sys_ode := diff(xhat(vars), a_1) = a_3*x + a_1, diff(yhat(vars), a_1) = a_2 - a_4*y + f(x), diff(uhat(vars), a_1) = a_3*u + 2*a_4*u, diff(vhat(vars), a_1) = a_4*v + diff(f(x), x)*u;

initvars := x, y, u, v, 0, a_2, a_3, a_4, f(x);
ics := xhat(initvars) = x, yhat(initvars) = y, uhat(initvars) = u, vhat(initvars) = v;
solution_a1 = dsolve([sys_ode, ics], [xhat, yhat, uhat, vhat]);

Can anyone help regarding this issue ?

Hello!

how to find the solutions of a system of recursive equations? And the plot too.

I tried but...

B := rsolve({a(0) = 0, a(i) = (1 + 10^(-5)*(0.01*(i - 1) - 0.007)/0.0001)*a(i - 1) + 0.1*10^(-5)*c(i - 1), c(0) = 0, c(i) = 0.01*10^(-5)*(i - 1)/0.0001*a(i - 1) + (1 - 10^(-5))*0.1*c(i - 1)}, {a(i), c(i)}, 'genfunc'(t));
B := rsolve({a(i) = (0.9983000000 + 0.001000000000 i) a(i - 1)

   + 0.000001000000000 c(i - 1), 

  c(i) = 0.001000000000 (i - 1) a(i - 1) + 0.09999900000 c(i - 1)

  }, {a(i), c(i)}, genfunc(t))

rsolve_for_system_of_recursive_equations.mw

thanks

I am trying to start writing small procedures in Maple. In the attached document I do not get an answer and I do not understand why. For clarity I have also added a working construct from another program so anyone willing to help me out can better understand what I am after.

Thanks in advance for assistance.

CDI_T_cor.mw

First of all I would like to wish everyone a happy, prosperous and especially healthy 2022!

I do not understand why my second formula in the attached sheet gives the wrong answers. I have added the correct answers in the vector "Correct". I still find it a bit cumbersome to work elementwise in Maple but that is most likely because still being relatively new to the program. Any help is more than appreciated 

Elementwise.mw 

Hi everyone. 

I need a program in maple to simulate the orbit of a satellite slowed down by the earth's atmosphere.

I chose the simple case, in which the orbits of the two are elliptical and I use The animation to do this. In this case I did not consider that the satellite interacts with the atmosphere.

Now,  I need equations to write part of the program in which I think the satellite is slowed down by the earth's atmosphere. I don't have any ideea to resolve this problem.

Soo.. I really need your' help as soon as posible.

Thank you a lot! 

# Below you find a small example about the function diffdiameter(conc,number), which has the unit length as long as the second argument number is not zero. Using the convert function it is possible to remove the units entirely, but this does not help, if I want to plot the functions. Is there a possibilty to plot diffdiameter(conc,number-not-zero) and diffdiameter(conc,0) in one diagramm? with(Units[Simple]); with(plots); diffdiameter := (conc, number) -> -number*diameter*exp(-conc/Unit(mol/kg)); diffdiameter := proc (conc, number) options operator, arrow; Units:-Simple:-`-`(Units:-Simple:-`*`(Units:-Simple:-`*`(numb\ er, diameter), Units:-Simple:-exp(Units:-Simple:-`-`(Units:-Si\ mple:-`*`(conc, Units:-Simple:-`/`(Unit(Units:-Simple:-`*`(mol\ , Units:-Simple:-`/`(kg))))))))) end proc diameter := 2*Unit(m); diameter := 2 Unit(m) evalf(diffdiameter(Unit(mol/kg), 6)); evalf(diffdiameter(Unit(mol/kg), 0)); -4.414553294 Unit(m) 0. convert(evalf(diffdiameter(Unit(mol/kg), 6)), unit_free); convert(evalf(diffdiameter(Unit(mol/kg), 0)), unit_free); -4.414553294 0. plot([convert(evalf(diffdiameter(conc, 0.001)), unit_free), convert(evalf(diffdiameter(conc, 6)), unit_free)], conc = 0 .. 4*Unit(mol/kg), title = "derivative Diameter with conc", labels = ["concentration / mol/kg", "deriv diameter / m"], color = ["blue", "red"], legend = ["bare diameter", "PLUS diameter"], labeldirections = ["horizontal", "vertical"], titlefont = [Helvetica, bold, 16], axesfont = [Helvetica, 14], labelfont = [Helvetica, 14], axes = boxed); plot([convert(evalf(diffdiameter(conc, 0)), unit_free), convert(evalf(diffdiameter(conc, 6)), unit_free)], conc = 0 .. 4*Unit(mol/kg)); Error, (in plot) invalid subscript selector

Under maple 2019 (linux ubuntu) I cannot make 3d plots !

Typing

plotd3d(sin(x*y),x=0..2,y=0..0.5);

does not produce any output and also the worksheet does not react any more. The only way to get out is to quit.

Btw: 2d plots work fine ...

What is wrong ? Thank you. Bs regards, Malte.

HOW TO DECIDE THE TRIPLE INTEGRAL IS POSITIVE, NEGATIVE OR ZERO WITHOUT CALCULATING IT?

Help.mw

How to put a function in the ODE. I have attached below work here.

Thank you

Download Help.mw

In the past I worked with mathcad where it was very easy to work with units. Now I try to switch to Maple but I am still struggling when I want to implement units. In the simple attached worksheet I try to multiply vector a in [m] with vector b in [cm]. I get an answer in [m] but I cannot convert the answer to another unit. Right clicking allows me to change the unit e.g. to mm but nothing happens in the worksheet. When I use convert, the units are expressed numerical in cm but the vector still shows m. My apologies in advance for this simple questions but I find no way to solve my issue.

CollabExample.mw

I am trying to use type(sqrt(t)*Y[1, -3]*Y[2, -6], monomial) to check if an expression is a monomial. But it returns false which is not correct. How to check that an expression in Maple is a monomial? Thank you very much.

Dear All, If I understood well dsolve uses the RK45 method to solve an ODE. I would like to compare the results of tha attached worksheet with the results of another software that uses RK4 as a standard. Can I adapt my worksheet to use RK4 and how do you do that? Thanks in advance for your willingness to help me out.QMP_Nov21.mw

I have the following code. I want to do the modify it so that:

1. The outputs of each for loop are merged in such a way that the outputs from the first loop (Es) that are also outputs of the second loop (Fs) are removed from the outputs of (Es).

2. The resulting outputs G= .... are saved to a text file, one to each line.

3. In between each output, I want to add 5 lines of text and a blank line, say

text1 text2 text3

text2 text2 text3

text3 text3 text3

text4 text4 text4

text5 text5 text5

(blank line)

so that in the text file, the format is (e.g.)

G={{1,2}};

text1 text2 text3

text2 text2 text3

text3 text3 text3

text4 text4 text4

text5 text5 text5

(blank line)

G={{1,2},{1,3}};

text1 text2 text3

text2 text2 text3

text3 text3 text3

text4 text4 text4

text5 text5 text5

(blank line)

etc.

What is the easiest way to accomplish this?

restart;
 
with(GraphTheory):
 n:= 4:
  L:= NonIsomorphicGraphs
      ( n,
        output=iterator,
        outputform=graph):
  Es:= Array
       ( [ seq
           (  Edges( L() ),
              j=1..NonIsomorphicGraphs
                   ( n,
                     output=count
                   )
           )
         ]
       ):


  M:= NonIsomorphicGraphs
      ( n-1,
        output=iterator,
        outputform=graph):
  Fs:= Array
       ( [ seq
           (  Edges( M() ),
              j=1..NonIsomorphicGraphs
                   ( n-1,
                     output=count
                   )
           )
         ]
       ):
;

numelems(Es): 
for i from 1 to numelems(Es) do G:=Es[i]:  od;
                           
numelems(Fs):
for i to numelems(Fs) do G := Fs[i]; od;
                        

elctroWav.mw have the equation 1 :

eq1 := 2*m*(E + e0^2/(rb*rho))*g(rho, t)*(-rb*rho + R)/(h^2*R) + R*(diff(g(rho, t), rho, rho)*(-rb*rho + R)/R - 2*diff(g(rho, t), rho)*rb/R)/(rb^3*rho) - diff(g(rho, t), t, t)*(-rb*rho + R)/(a^2*c^2*R) = 0;

with iv1:

iv1 := D[1](g)(0, 0) - g(0, 0)*rb/R = rb*R, g(1, 0)*(R - rb)/R = 0, D[2](g)(rb, 0) = a*c;

As in maple document electroWav.mw

The issue is that there is an unsolved part with RootOf how can I rezolve it?

-R*h^2*RootOf(AiryBi(-(R*_Z^3*h^2 + 2*e0^2*m*rb^2)/(_Z^2*R*h^2)))^3

Please advice...

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