Maple Questions and Posts

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restart;
Pr:=0.71: n:=-1:

eta0:=0.0699;

EQ1:=diff(H(x), x ) - x*diff(F(x), x ) ;
 

EQ2:=(1+x^2)*diff(F(x), x$2) + (3*x + x*F(x)-H(x))*diff(F(x), x) + F(x)^2 + G(x)^2 +2*P(x) + x*diff(P(x), x) ;

EQ3:=(1+x^2)*diff(G(x), x$2) + (3*x + x*F(x)-H(x))*diff(G(x), x) ;

EQ4:=(1+x^2)*diff(H(x), x$2) + (3*x + x*F(x)-H(x))*diff(H(x), x) + (1+F(x))*H(x)- diff(P(x), x);

EQ5:=(1+x^2)*diff(theta(x), x$2) + x*(1-2*n)*diff(theta(x), x) + n^2*theta(x) - Pr*( n*F(x)*theta(x) + ( H(x)-x*F(x) )*diff(theta(x), x)  ) ;


EQ:={EQ1=0, EQ2=0,EQ3=0,EQ4=0 ,EQ5=0}:


IC:={ F(0)=0, G(0)=12, H(0)=0, theta(0)= 1, F(eta0)=0, G(eta0)=12, H(eta0)=0, theta(eta0)= 0, P(0)=0};
 

sol:= dsolve(EQ union IC,numeric,output=Array([0,0.0699]));

ques.mw

HPM.mw

  • Please help me
  • How do I write Homotopy Perturbation method for a partial differential equation for this question in Maple?

Download HPM.mw

 

dS/dt=qnv-alpha_1*S*H-mu_sh*S

dH/dt=lamda_h-alpha_1*S*H-mu_h*H

dI/dt=alpha_1*S*H-beta_1*I-mu_i*I

dS/dt=beta_1*I-delta_1*S-mu_s*S

DATA:

q=0.75; n=15;v=20; alpha_You1=0.001; S=2000; H=3000; mu_sh=0.000000000012; lambda=3000;mu_h=0.94; beta_1=0.125; I=0; mi_i=0.95; delta_1=0.0975; S=0; mu_s=0.029

Good day all,

please I am new Maple user, i used the same code to solve boundary layer flow. Itried to use the same code in solving nanofluid but the solution is not coverging at some point. But the author i want to compared my results with had solution at those points.

Is there any way i can get solution of this model at this with these values?. Please i need your help. Thank you in advance

secod_code.mw

NULL

restart

with*plots; ode1 := (1+1/bet)*(diff(f(eta), eta, eta, eta))-(diff(f(eta), eta))^2+f(eta)*(diff(f(eta), eta, eta))+Gr*(theta(eta)+lambda1*theta(eta)^2)+Gc*(phi(eta)+lambda2*phi(eta)^2)-M*(diff(f(eta), eta)) = 0

(1+1/bet)*(diff(diff(diff(f(eta), eta), eta), eta))-(diff(f(eta), eta))^2+f(eta)*(diff(diff(f(eta), eta), eta))+Gr*(theta(eta)+lambda1*theta(eta)^2)+Gc*(phi(eta)+lambda2*phi(eta)^2)-M*(diff(f(eta), eta)) = 0

(1)

ode2 := (diff(theta(eta), eta, eta))*(1+(4*R*(1/3))*(theta(eta)+CT)^3)/Pr+4*R*(theta(eta)+CT)^2*(diff(theta(eta), eta))^2+f(eta)*(diff(theta(eta), eta))+Nb*(diff(phi(eta), eta))*(diff(theta(eta), eta))+Nt*(diff(theta(eta), eta))^2-de*(f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta))+f(eta)^2*(diff(theta(eta), eta, eta))) = 0

(diff(diff(theta(eta), eta), eta))*(1+(4/3)*R*(theta(eta)+CT)^3)/Pr+4*R*(theta(eta)+CT)^2*(diff(theta(eta), eta))^2+f(eta)*(diff(theta(eta), eta))+Nb*(diff(phi(eta), eta))*(diff(theta(eta), eta))+Nt*(diff(theta(eta), eta))^2-de*(f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta))+f(eta)^2*(diff(diff(theta(eta), eta), eta))) = 0

(2)

ode3 := diff(phi(eta), eta, eta)+Pr*Le*(diff(phi(eta), eta))*f(eta)+Nt*(diff(theta(eta), eta, eta))/Nb-Pr*Le*dc*(f(eta)*(diff(f(eta), eta))*(diff(phi(eta), eta))+f(eta)^2*(diff(phi(eta), eta, eta))) = 0

diff(diff(phi(eta), eta), eta)+Pr*Le*(diff(phi(eta), eta))*f(eta)+Nt*(diff(diff(theta(eta), eta), eta))/Nb-Pr*Le*dc*(f(eta)*(diff(f(eta), eta))*(diff(phi(eta), eta))+f(eta)^2*(diff(diff(phi(eta), eta), eta))) = 0

(3)

bcs1 := f(0) = 0, (D(f))(0) = 1+xi*((D^2)(f))(0), (D(f))(6) = 0, theta(6) = 0, phi(0) = 1+`ς`*(D(phi))(0), theta(0) = 1+Zeta*(D(theta))(0), phi(6) = 0

f(0) = 0, (D(f))(0) = 1+xi*(D(f))(0)^2, (D(f))(6) = 0, theta(6) = 0, phi(0) = 1+varsigma*(D(phi))(0), theta(0) = 1+Zeta*(D(theta))(0), phi(6) = 0

(4)

NULL

 

L := [0., .1, .4, 1]

[0., .1, .4, 1]

(5)

 
  

NULL


  for k to 10 do
      sol_All := dsolve
                 ( eval
                   ( {bcs1, ode1, ode2,ode3},
                     [xi= L[k],R=1, CT=0.2, Gr=0.5, Gc=0.5, lambda1=0.2, lambda2=0.2, Pr=0.72, Nb=0.5,  Le=1, dc=0.2, de=0.2, Nt=0.5, Zeta=0.5, varsigma=0.5, M=1.5, bet=1.5]
                   ),
                   [f(eta), theta(eta),phi(eta)],
                   numeric,
                   output = listprocedure
                 );
      Y_sol || k := rhs(sol_All[5]);
      YP_sol || k := -rhs(sol_All[6]);

feta || k := rhs(sol_All[4]);
      fpeta || k := rhs(sol_All[3]);

phieta || k := rhs(sol_All[8]);
      phipeta || k := rhs(sol_All[7])
  end do:

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

 

for k to 10 do L[k], [(Y_sol || k)(0), (YP_sol || k)(0)] end do

0., [Y_sol1(0), YP_sol1(0)]

 

.1, [Y_sol2(0), YP_sol2(0)]

 

.4, [Y_sol3(0), YP_sol3(0)]

 

1, [Y_sol4(0), YP_sol4(0)]

 

Error, invalid subscript selector

 

for k to 10 do L[k], [(feta || k)(0)] end do

0., [feta1(0)]

 

.1, [feta2(0)]

 

.4, [feta3(0)]

 

1, [feta4(0)]

 

Error, invalid subscript selector

 

NULL

Error, mismatched or missing bracket/operator

"for k  from 1 to  10 do L[k], ([phieta ||k(0),phipeta||k(0)]); od; "

 

NULL

  plot( [ seq((Y_sol||j)(eta), j = 1..6)],
         eta = 0 .. 6,
         labels = [eta, theta(eta)],
         axes = boxed
      );
plot( [ seq((YP_sol||j)(eta), j = 1..6)],
         eta = 0 .. 8,
         labels = [eta, thetaprime(eta)],
         axes = boxed
      );

 plot( [ seq((feta||j)(eta), j = 1..6)],
         eta = 0 .. 8,
         labels = [eta, f(eta)],
         axes = boxed
      );
  plot( [ seq((fpeta||j)(eta), j = 1..6)],
         eta = 0 .. 5,
         labels = [eta, fprime(eta)],
         axes = boxed
      );
plot( [ seq((phipeta||j)(eta), j = 1..6)],
         eta = 0 .. 5,
         labels = [eta, phiprime(eta)],
         axes = boxed
      );

plot( [ seq((phieta||j)(eta), j = 1..6)],
         eta = 0 .. 5,
         labels = [eta, phi(eta)],
         axes = boxed
      );

Warning, expecting only range variable eta in expression Y_sol1(eta) to be plotted but found name Y_sol1

 

 

Warning, expecting only range variable eta in expression YP_sol1(eta) to be plotted but found name YP_sol1

 

 

Warning, expecting only range variable eta in expression feta1(eta) to be plotted but found name feta1

 

 

Warning, expecting only range variable eta in expression fpeta1(eta) to be plotted but found name fpeta1

 

 

Warning, expecting only range variable eta in expression phipeta1(eta) to be plotted but found name phipeta1

 

 

Warning, expecting only range variable eta in expression phieta1(eta) to be plotted but found name phieta1

 

 

How to conver a patial differetial equation to ordinary differential equation with or without dchange?
 

restart

declare(u(x, y, t), v(x, y, t), T(x, y, t), C(x, y, t), eta(x, y, t), psi(x, y, t), f(eta), theta(eta), phi(eta));

declare(u(x, y, t), v(x, y, t), T(x, y, t), C(x, y, t), eta(x, y, t), psi(x, y, t), f(eta), theta(eta), phi(eta))

(1)

eta := proc (x, y, t) options operator, arrow; y/(nu*t+nu*x/U[w])^(1/2) end proc:

eq1 := diff(T(x, y, t), t)+u*(diff(T(x, y, t), x))+v*(diff(T(x, y, t), y))-sigma*(diff(T(x, y, t), y, y))-epsilon*D[B]*(diff(T(x, y, t), y))*(diff(C(x, y, t), y)) = 0

diff(T(x, y, t), t)+U[w]*(D(f))(y/(nu*t+nu*x/U[w])^(1/2))*(diff(T(x, y, t), x))+(-(1/2)*f(y/(nu*t+nu*x/U[w])^(1/2))*nu/(nu*t+nu*x/U[w])^(1/2)+(1/2)*(D(f))(y/(nu*t+nu*x/U[w])^(1/2))*y*nu/(nu*t+nu*x/U[w]))*(diff(T(x, y, t), y))-sigma*(diff(diff(T(x, y, t), y), y))-epsilon*D[B]*(diff(T(x, y, t), y))*(diff(C(x, y, t), y)) = 0

(2)

``


 

Download pde_to_ode.mw

Dear Maple experts,

I am running a Maple code with several lines/ curves in a plot.

For two of the curves, I use style=pointline. But in the legend the symbols on the lines are not shown. Can you advise how we can make them appear?

I have attached the file. Thank you so much! 

Download LegendPlot.mw

When i try to log on to my maplesoft acount on Maple 2023 i get a messeage saying "Sign in Error: Please check your credentials and try again." i have done this multiple time double checked my password and everything, but it won't let me log on... what do i do?

Hi @Acer, and of course also hi to the whole mapleprimes comunnity.

I have a problem with the Phasors module. Very often I have to use the evalc in calculations involving phasors. Sometimes it might make sense, since one of the involved variables are not defined as a phasor.

May I suggest that you upgrade the phasors module to a package Acer? I'd be honored to help in the testing.

Besides I have the same experience as mentioned in this question (bear over with me it's years since already): Maple 2020 Sheet now opening in 2021, 2022, and 2023 results in errors.

 

attached some examples:

Eksempel_8.2.mw

Example_12.3.mw

Eksempel_14.5.mw

Opgave_4_-_SHS_-_RA_ref-UL1.mw

Opgave_4_-_SHS_-_RA_ref-UL1_using_context_menu.mw

Hi,

I'm just working on som electricity tasks and have to calculate thre phase power in alternating current systems. I use the SI system and have checked that with UsingSystem() -> SI and GetUnits() -> voltampere[power], voltampere_reactive[power] among others, so everything should be alright, but why can't I then choose theese units from neither the Units Palette, the Context Panel or right click menu option Convert Output Units?

convert(expr, units, var) and convert(expr, units, VA) works but my students and colleagues won't be satisfied with that.

Thank you for any help.

Is there a way to delete frames arround the legend in a plot?

I have a calculation sheet that used to work in Maple 2020 and earlier, but with an upgrade to versions 2021 to 2023 the same errors are appearing. The sheet still functions fine in 2020 but unknown why these errors appear when using 2021 thru 2023.

Does anyone know what might have changed with the later versions to result in these types of errors?

Hi . My question is about writing a gravity equation, which I explained comprehensively I  explain in the PDF linked below, and I need the code for this equation in Maple.

My_Question2.pdf

I am currently unable to type in maple 2021, there is no cursor, nothing shows up when I type etc. I am also unable to save files. I went into document mode, nothing. Some of the dialogs don't show up. Where does maple save documents and how do I change that setting? That might be my problem. Furthermore, there are no tabs visable, like I can't access any documents I open.

Hi,

Im trying to configure Maple's colors by modifying the X11_defaults/Maple file but nothing happens. I set the environment variable MAPLE to point to my Maple installation and load the previous file with xrdb. I am running dwm as my window manager in Arch Linux.

I am frustrated. All help is welcomed. If you have any suggestion for configuring dark mode in a different way, please share your arcane knowledge with me.

Thank you in advance.

I am slightly confused as I can't apply the seemingly correct function to a sequence. It seems like modp does not like my inverse. But I am not aware of any other way of finding the modular inverse.  

a := i -> (1025 - 2^(10 - 2^i))^(-1) mod (1025 - 2^(10 - 2*2^i));

proc (i) options operator, arrow; `mod`(1/(1025-2^(10-2^i)), 1025-2^(10-2*2^i)) end proc

(1)

a(1);

5

(2)

a(2);

17

(3)

map(i -> i + 1, {seq(1 .. 4)});

{2, 3, 4, 5}

(4)

map(i -> 1/(1025 - 2^(10 - 2^i)) mod (1025 - 2^(10 - 2*2^i)), {seq(1 .. 4)});

Error, invalid input: modp received 65599/64, which is not valid for its 2nd argument, m

 

map(a, {seq(1 .. 4)});

Error, invalid input: modp received 65599/64, which is not valid for its 2nd argument, m

 

NULL

NULL

Download example.mw

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