MaplePrimes Questions

I am very new to Maple and am wondering how i would install a package. The package I am trying to install is located at

http://math.rutgers.edu/~russell2/papers/IdentityFinder 

I am using Maple 2015 on windows 8. Any advice would be useful

Good day everyone,

please how can one solve this pde in terms of Bessel function or any other analytic solution with the plot.

See the file ID.mw

Thanks.

I am currently learning about nonlinear waves and and am having problems with my maple coding where I am plotting the characteristics of the initial value problem

$u_[t] + uu_[x] = 0$ where $u(x,t) = a$ if $x < -1$

                                               = $b$ if $ -1 < x < 1$

                                               = $c$ if $ x > 1$

where $a$, $b$ and $c$ are unequal constants. Also, there are 6 cases to this, $a > b > c$, $a > c > b$, $b > a >c$, $b > c > a$, $c > a > b$ and $c > b > a$. In each case I need to plot the characteristics (and where possible plot the rarefaction waves, but this bit is not necessary right now). My problem is that I am highly certain that my code is incorrect as I am unsure where/how to implement the fact that $a$, $b$ and $c$ vary since there are different cases. My current code is down below

 

 

restart: with(plots): with(plottools): with(PDEtools):
ploti:= implicitplot({seq(t*((k/2))+k/2-x,k=-10..-1)},x=-10..10,t=0..10,view=[-5..5,0..5],color=blue,thickness=2):
ploti2:= implicitplot({seq(t*(k/2)+k/2-x,k=-1..1)},x=-10..10,t=0..10,view=[-5..5,0..5],color=red,thickness=2):
ploti3:= implicitplot({seq(t*((k/2))+k/2-x,k=1..10)},x=-10..10,t=0..10,view=[-5..5,0..5],color=yellow,thickness=2):
display(ploti,ploti2,ploti3);

Any help would be much appreciated

 


 \int_{a}^{b} f(x) \, dx \approx \tfrac{3h}{8}\left[f(x_0) + 3f(x_1) + 3f(x_2) 
+ 2f(x_3) + 3f(x_4) + 3f(x_5) + 2f(x_6) + ... + f(x_n)\right] .


A Fantastic Good morning Ladies and Gentelmen,

You have the mission to find the problem in that code/ give a better code?
I want to write a procedure for the simpson 3/8 rule using the above formula I took from wikipedia :
(I don't want to use any super maple command that estimate the simpson 3/8, but just using this formula and starting from scratch, I am a beginner so feel free to laugh at my code hehehe)
here is the code I managed to write after 365 hours :D

restart:
simp38:=proc(f,x0,xn,n)                 
     local h,summ,i,x,Integral:                                              
     h=evalf((xn-x0)/n);               #h is the distance between 2 points
     summ:=f(x0)+f(xn);              #initialise the summ
    
      for i from 1 to n-1 by 3 do             
          x[i]:=x0+i*h:
          summ:=evalf(summ+3*f(x[i])):
      od:
      for i from 2 to n-1 by 3 do              
          x[i]:=x0+i*h:
          summ:=evalf(summ+3*f(x[i])):
      od:
      for i from 3 to n-1 by 3 do                  
          x[i]:=x0+i*h:
          summ:=evalf(summ+2*f(x[i])):  
      od:
    
      Integral:=3*h/8*summ;                  
 end:

simp38(x->(x^5-5.15*x^2+8.55*x-4.05045),1,5,6);   #testing it      --->2481.087090
evalf(int(x^5-5.15*x^2+8.55*x-4.05045,x=1..5));      #comparing it --->2477.531533


Your help will be apreciated.


Hi

Do the following equation solve by method of line(MOL) with this software?

du/dt=0.01 d^2u/dx^2

conditions:

u(x,0)=10

u(0,t)=0

u(1,t)=0

t=1,delta t=0.1,x=1,Nx=10

thank you

hello everyone, I have problem in my project written by matlab to solving my equations with rang-kuta 4 order method. I send my project file.  please help me to run it correctly. thank you.

input Q_j n j V Z F_ve a_1 a_2 p_1 p_2 L A f m k c h t i;

for jj=1:n;

            s=Q_j(jj);

end

b=(-V)*Z;

o=(F_ve*A)*(((a_1^2)*p_1)-((a_2^2)*p_2))/L;

% RK4 method;

% md2z/dt2+cdz/dt+kz=f;

% dz_1/dt=z_2;

% mdz_2/dt+cdz_1/dt+z_1k=f;

% dz_2/dt=1/m(f-cz_2-kz_1);

f=0;

m=1;

k=s+b+o;

c=0;

h=0.5;

t=0:0.5:t;

z1=zeros (1,n);

z2=zeros (1,n);

z1 (1)=0;

z2 (1)=1;

% N=length (t);

f1=@(t,z1,z2)z2;

f2=@(t,z1,z2)f-(c*z2)-(k*z1);

for i=1:n-1;

    k1=f1 (t (i),z1 (i),z2 (i));

    m1=f2 (t (i),z1 (i),z2 (i));

    k2=f1 (t (i)+h/2,z1 (i)+0.5*k1*h,z2 (i)+0.5*m1*h);

    m2=f2 (t (i)+h/2,z1 (i)+0.5*k1*h,z2 (i)+0.5*m1*h);

    k3=f1 (t (i)+h/2,z1 (i)+0.5*k2*h,z2 (i)+0.5*m2*h);

    m3=f2 (t (i)+h/2,z1 (i)+0.5*k2*h,z2 (i)+0.5*m2*h);

    k4=f1 (t (i)+h,z1 (i)*k3*h,z2 (i)*m3*h);

    m4=f2 (t (i)+h,z1 (i)*k3*h,z2 (i)*m3*h);

    z1 (i+1)=z1 (i)+(h/6)*(k1+(2*k2)+(2*k3)+k4);

    z2 (i+1)=z2 (i)+(h/6)*(m1+(2*m2)+(2*m3)+m4);

end

plot (t,z1)

plot (t,z2)

plot (z,t)

 

 

 

 


can anybody help me..? why my graph not come out? Is that any mistake in my coding?

restart

y := x^2-x*(exp(I*k*`&Delta;x`)+exp(-I*k*`&Delta;x`)-m^2+m^2*((4*((1^2-2)*cosh(1+1)-4*sinh(1+1)+1^6*cosh(1+1)^3))*((1^2-2)*cosh(1+1)-4*sinh(1+1)+1^6*cosh(1+1)^3)*((1^2-2)*cosh(1+1)-4*sinh(1+1)+1^6*cosh(1+1)^3))*((1^2-2)*cosh(1+1)-4*sinh(1+1)+1^6*cosh(1+1)^3)/(epsilon*((((1^2-2)*cosh(1+1)-4*sinh(1+1)+1^6*cosh(1+1)^3)*((1^2-2)*cosh(1+1)-4*sinh(1+1)+1^6*cosh(1+1)^3))*((1^2-2)*cosh(1+1)-4*sinh(1+1)+1^6*cosh(1+1)^3+((1^2-2)*cosh(1+1)-4*sinh(1+1)+1^6*cosh(1+1)^3))+(((1^2-2)*cosh(1+1)-4*sinh(1+1)+1^6*cosh(1+1)^3)*((1^2-2)*cosh(1+1)-4*sinh(1+1)+1^6*cosh(1+1)^3))*((1^2-2)*cosh(1+1)-4*sinh(1+1)+1^6*cosh(1+1)^3+((1^2-2)*cosh(1+1)-4*sinh(1+1)+1^6*cosh(1+1)^3)))))+1;

x^2-x*(exp(I*k*`&Delta;x`)+exp(-I*k*`&Delta;x`)-m^2+2*m^2*(-cosh(2)-4*sinh(2)+cosh(2)^3)^2/(epsilon*(-2*cosh(2)-8*sinh(2)+2*cosh(2)^3)))+1

(1)

subs(m = 1-exp(-m), %);

x^2-x*(exp(I*k*`&Delta;x`)+exp(-I*k*`&Delta;x`)-(1-exp(-m))^2+2*(1-exp(-m))^2*(-cosh(2)-4*sinh(2)+cosh(2)^3)^2/(epsilon*(-2*cosh(2)-8*sinh(2)+2*cosh(2)^3)))+1

(2)

subs(epsilon = .17882484, %);

x^2-x*(exp(I*k*`&Delta;x`)+exp(-I*k*`&Delta;x`)-(1-exp(-m))^2+11.18412856*(1-exp(-m))^2*(-cosh(2)-4*sinh(2)+cosh(2)^3)^2/(-2*cosh(2)-8*sinh(2)+2*cosh(2)^3))+1

(3)

subs(k = n*Pi, %);

x^2-x*(exp(I*n*Pi*`&Delta;x`)+exp(-I*n*Pi*`&Delta;x`)-(1-exp(-m))^2+11.18412856*(1-exp(-m))^2*(-cosh(2)-4*sinh(2)+cosh(2)^3)^2/(-2*cosh(2)-8*sinh(2)+2*cosh(2)^3))+1

(4)

subs(`&Delta;x` = m, %);

x^2-x*(exp(I*n*Pi*m)+exp(-I*n*Pi*m)-(1-exp(-m))^2+11.18412856*(1-exp(-m))^2*(-cosh(2)-4*sinh(2)+cosh(2)^3)^2/(-2*cosh(2)-8*sinh(2)+2*cosh(2)^3))+1

(5)

subs(m = 0.1e-2, %);

x^2-x*(exp((0.1e-2*I)*n*Pi)+exp(-(0.1e-2*I)*n*Pi)-(1-exp(-0.1e-2))^2+11.18412856*(1-exp(-0.1e-2))^2*(-cosh(2)-4*sinh(2)+cosh(2)^3)^2/(-2*cosh(2)-8*sinh(2)+2*cosh(2)^3))+1

(6)

j := subs(n = 1, %);

x^2-x*(exp((0.1e-2*I)*Pi)+exp(-(0.1e-2*I)*Pi)-0.9990006498e-6+0.1117295170e-4*(-cosh(2)-4*sinh(2)+cosh(2)^3)^2/(-2*cosh(2)-8*sinh(2)+2*cosh(2)^3))+1

(7)

complexplot3d(x*j, x = -2-I .. 2+I);````

complexplot3d(x*(x^2-x*(exp((0.1e-2*I)*Pi)+exp(-(0.1e-2*I)*Pi)-0.9990006498e-6+0.1117295170e-4*(-cosh(2)-4*sinh(2)+cosh(2)^3)^2/(-2*cosh(2)-8*sinh(2)+2*cosh(2)^3))+1), x = -2-I .. 2+I)

(8)

a := fsolve(x*j, x);

0., .9865070072, 1.013677544

(9)

b := fsolve(x*j, x = 1);

0., .9865070072, 1.013677544

(10)

with(plots):

complexplot({a, b}, numpoints = 100, color = green, filled = true, title = "Stability Region");

 

``

``

``


Download Stability_1.mw

Hi everyone!

I use two "ArrayTools:-Copy" commands to copy elements from Vector A to Vector B.

restart;
A := LinearAlgebra:-RandomVector(10); A := convert(A, Vector[row]);
B := Vector[row](10); ArrayTools:-Copy(2, A, 1, B, 1); ArrayTools:-Copy(2, A, 7, B, 7); B;

My question is: Could I obtain the same result using only one command?

P.S. I tried to use "ArrayTools:-BlockCopy", but didn't get correct result.

 

I want to retrieve all the commands input by user in a maple document saved on disk. How this can be done? DocumentTools:-Retrieve permits to receive only the labeled expressions but not the input commands.

The following error occurred when I simulate a build-in model, anyone could help me to solve this problem? Thanks first

Hi
how can we write a same result n-times near each other


x:=3:
for i from 1 to 4 do       # here the 4 can be a variable and can change...
    x;
    od;
                                  3
                                  3
                                  3
                                  3

I need the result to come in that form  :    3  ,  3  ,  3  ,  3
and because the number of times can change i can't just easily write x,x,x,x;

thanks in advance

guys, i put a test solution in my differential equation and when i excuted it, maple calculated the solution in term of functions itself. 

i mean, i have functions A(r),B(r),C(r),phi(r) in a differential equation and then i put A(r)=(1-a/r)^alpha and B(r)=(1-a/r)^beta and C(r)=(1-a/r)^gamma and phi(r)=Q*(1-a/r)^lambda , maple give me result with A and B and ... . i want to maple give the result with out any function and just in term of (1-a/r)^... and alpha , betta , .... and c

and is there any way to arrange in term of power of (1-a/r)^... or something like that ?

what is your opnion ?

 

and also i obtained the differential equation by maple and it is not simplify completely and some terms can cancel each other how can i simplify it completely?

thanks in advance

 

de.mw

worksheet/expressions/copypasteMaple

Gerschgorin := proc (A::Matrix) local Delta, m, n, AA, R, C, i, c, eig, P, Plt; Delta := proc (i, j) if i = j then 0 else 1 end if end proc; m, n := LinearAlgebra[Dimension](A); AA := Matrix(m, n, proc (i, j) options operator, arrow; Delta(i, j)*abs(A[i, j]) end proc); R := evalm(`&*`(AA, Vector(m, 1))); C := {seq(('plottools[circle]')([Re(A[i, i]), Im(A[i, i])], R[i], color = violet), i = 1 .. m)}; c := {seq(('plottools[point]')([Re(A[i, i]), Im(A[i, i])], color = blue, symbol = diamond), i = 1 .. m)}; eig := evalf(LinearAlgebra[Eigenvalues](A)); P := {seq(('plottools[point]')([Re(eig[i]), Im(eig[i])], color = red, symbol = box), i = 1 .. m)}; Plt := `union`(`union`(C, c), P); plots[display](eval(Plt), scaling = constrained) end proc

 

A := Matrix([[5, 8, 4, -3], [8, -9, 7, 5], [0, 4, 4, 2], [5, -5, 9, -9]]); evalf(LinearAlgebra[Eigenvalues](A), 3); Gerschgorin(A)

worksheet/expressions/pasteMathML

 

F := Matrix([[2, -1/2, -1/3, 0], [0, 6, 1, 0], [1/3, -1/3, 5, 1/3], [-1/2, 1/4, -1/4, 4]]); evalf(LinearAlgebra[Eigenvalues](F)); Gerschgorin(F)

Could you print A & F ?

 

regards

 

 

Hello i would love some help with this code i need Maple to make an exercise guide in word automaticly the thing is that i don't know how to automaticly insert the plot in the word, i think there is no fprintf format to add images or plots maybe with exportplot? i really don't know; here is the Code is Basic for a starter student i just need the comand to insert the plot just that.
-------------------------------------------------------------------
fd:fopen("Graphs.doc", WRITE);
 for i from 1 by 5 to 11do
  if i=1 then plotsetup(bmp,plotoutput=plot1);
 a:= -50;
 b:=30;
 elif i=6 then
 plotsetup(bmp,plotoutput=plot2);
 a:= 50;
 b:=-30;
  elif i=11 then  plotsetup(bmp,plotoutput=plot3);
  a:= 2;
 b:=-3;
 end if;
 h:=(i*x^(2)-((3*a)/(i-42))*x-(i*b)/(-i+42));
  fprintf(fd,"the quadratic equation is: ")
fprintf(fd,"%q \\n",h);
 #`HERE IS WHERE I NEED THE PLOT TO BE`
  plot(i*x^(2)-((3*a)/(i-42))*x-(i*b)/(-i+42),x)
   end do; 
 fclose(fd);
--------------------------------------------------------------------
pd. i can't do it manually i need it to be automatic later i will add some inputs to make it even faster.

Hi, as I can't manage to copy and paste on mapleprimes, I would be glad to get a hint ...

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