Maple 16 Questions and Posts

These are Posts and Questions associated with the product, Maple 16

PDE := diff(u(x, y), x, x)+diff(u(x, y), y, y)-6*x*y*(1-y)-2*x^3 = 0; BCsx := u(xL, y) = 0, u(xU, y) = y*(1-y); BCsy := u(x, yL) = 0, u(x, yU) = 0; solPDE := pdsolve({BCsx, BCsy, PDE}, u(x, y)); exactSol := unapply(rhs(%), x, y)

Hi, i encountered this, error, and the link to the help page was broken.

Error, (in RootOf) expression independent of _S000100
 


Please help me on this :

restart; with(PDETools), with(plots)

n := .3:

Eq1 := (1-n)*(diff(f(x, y), `$`(y, 3)))+(1+x*cot(x))*f(x, y)*(diff(f(x, y), `$`(y, 2)))-(diff(f(x, y), y))/Da+(diff(f(x, y), y))^2+n*We*(diff(f(x, y), `$`(y, 2)))*(diff(f(x, y), `$`(y, 3)))+sin(x)*(theta(x, y)+phi(x, y))/x = x*((diff(f(x, y), y))*(diff(f(x, y), y, x))+(diff(f(x, y), `$`(y, 2)))*(diff(f(x, y), x))):

Eq2 := (diff(theta(x, y), `$`(y, 2)))/Pr+Nt*(diff(theta(x, y), y))^2/Pr+Nb*(diff(phi(x, y), y))*(diff(theta(x, y), y))/Pr+(1+x*cot(x))*f(x, y)*(diff(theta(x, y), y)) = x*((diff(f(x, y), y))*(diff(theta(x, y), x))+(diff(theta(x, y), y))*(diff(f(x, y), x))):

Eq3 := Nb*(diff(phi(x, y), `$`(y, 2)))/(tau*Pr)+Nt*(diff(theta(x, y), `$`(y, 2)))/(tau*Pr)+(1+x*cot(x))*f(x, y)*(diff(phi(x, y), y)) = x*((diff(f(x, y), y))*(diff(phi(x, y), x))+(diff(phi(x, y), y))*(diff(f(x, y), x))):

ValWe := [0, 5, 10]:

bcs := {Nb*(D[2](phi))(x, 0)+Nt*(D[2](theta))(x, 0) = 0, f(0, y) = ((1/12)*y)^2*(6-8*((1/12)*y)+3*((1/12)*y)^2), f(x, 0) = 0, phi(0, y) = -.5*y, phi(x, 12) = 0, theta(0, y) = (1-(1/12)*y)^2, theta(x, 0) = 1, theta(x, 12) = 0, (D[2](f))(x, 0) = Da^(1/2)*(D[2, 2](f))(x, 0)+Da*(D[2, 2, 2](f))(x, 0), (D[2](f))(x, 12) = 0}:

pdsys := {Eq1, Eq2, Eq3}:

p1 := ans[1]:-plot(theta(x, y), x = 1, color = blue):

plots[display]({p1, p2, p3})

 

``


 

Download untitle_2_(1).mw

Hi everyone. I'm going to solve a problem of an article with hpm. well I wrote some initial codes(I uploaded both codes and article). but now I face with a problem. I cant reach to the correct plot that is in the article. could you please help me???

(dont think I am lazy ;))) I found f and g (by make a system with A1 and B1 and solve it i found f[0] and g[0], with p^3 coefficient in A-->f[1] and then with B2 I foud g[1]) and their plot was correct. but the problem is theta and phi and their plots :(( )

Project.mw

2.pdf   this is article



 

restart;

lambda:=0.5;K[r]:=0.5;Sc:=0.5;Nb:=0.1;Nt:=0.1;Pr:=10;

.5

 

.5

 

.5

 

.1

 

.1

 

10

(1)

EQUATIONS

equ1:=diff(f(eta),eta$4)-R*(diff(f(eta),eta)*diff(f(eta),eta$2)-f(eta)*diff(f(eta),eta$2))-2*K[r]*diff(g(eta),eta)=0;

equ2:=diff(g(eta),eta$2)-R*(diff(f(eta),eta)*g(eta)-f(eta)*diff(g(eta),eta))+2*K[r]*diff(f(eta),eta)=0;

equ3:=diff(theta(eta),eta$2)+Pr*R*f(eta)*diff(theta(eta),eta)+Nb*diff(phi(eta),eta)*diff(theta(eta),eta)+Nt*diff(theta(eta),eta)^2=0;

equ4:=diff(phi(eta),eta$2)+R*Sc*f(eta)*diff(phi(eta),eta)+diff(theta(eta),eta$2)*(Nt/Nb)=0;

diff(diff(diff(diff(f(eta), eta), eta), eta), eta)-R*((diff(f(eta), eta))*(diff(diff(f(eta), eta), eta))-f(eta)*(diff(diff(f(eta), eta), eta)))-1.0*(diff(g(eta), eta)) = 0

 

diff(diff(g(eta), eta), eta)-R*((diff(f(eta), eta))*g(eta)-f(eta)*(diff(g(eta), eta)))+1.0*(diff(f(eta), eta)) = 0

 

diff(diff(theta(eta), eta), eta)+10*R*f(eta)*(diff(theta(eta), eta))+.1*(diff(phi(eta), eta))*(diff(theta(eta), eta))+.1*(diff(theta(eta), eta))^2 = 0

 

diff(diff(phi(eta), eta), eta)+.5*R*f(eta)*(diff(phi(eta), eta))+1.000000000*(diff(diff(theta(eta), eta), eta)) = 0

(2)

BOUNDARY*CONDITIONS

ics:=
f(0)=0,D(f)(0)=1,g(0)=0,theta(0)=1,phi(0)=1;
f(1)=lambda,D(f)(1)=0,g(1)=0,theta(1)=0,phi(1)=0;

f(0) = 0, (D(f))(0) = 1, g(0) = 0, theta(0) = 1, phi(0) = 1

 

f(1) = .5, (D(f))(1) = 0, g(1) = 0, theta(1) = 0, phi(1) = 0

(3)

HPMs

hpm1:=(1-p)*(diff(f(eta),eta$4)-2*K[r]*diff(g(eta),eta))+p*(diff(f(eta),eta$4)-R*(diff(f(eta),eta)*diff(f(eta),eta$2)-f(eta)*diff(f(eta),eta$2))-2*K[r]*diff(g(eta),eta))=0;

hpm2:=(1-p)*(diff(g(eta),eta$2)+2*K[r]*diff(f(eta),eta))+p*(diff(g(eta),eta$2)-R*(diff(f(eta),eta)*g(eta)-f(eta)*diff(g(eta),eta))+2*K[r]*diff(f(eta),eta))=0;

hpm3:=(1-p)*(diff(theta(eta),eta$2))+p*(diff(theta(eta),eta$2)+Pr*R*f(eta)*diff(theta(eta),eta)+Nb*diff(phi(eta),eta)*diff(theta(eta),eta)+Nt*diff(theta(eta),eta)^2)=0;

hpm4:=(1-p)*(diff(phi(eta),eta$2)+diff(theta(eta),eta$2)*(Nt/Nb))+p*(diff(phi(eta),eta$2)+R*Sc*f(eta)*diff(phi(eta),eta)+diff(theta(eta),eta$2)*(Nt/Nb))=0;

(1-p)*(diff(diff(diff(diff(f(eta), eta), eta), eta), eta)-1.0*(diff(g(eta), eta)))+p*(diff(diff(diff(diff(f(eta), eta), eta), eta), eta)-R*((diff(f(eta), eta))*(diff(diff(f(eta), eta), eta))-f(eta)*(diff(diff(f(eta), eta), eta)))-1.0*(diff(g(eta), eta))) = 0

 

(1-p)*(diff(diff(g(eta), eta), eta)+1.0*(diff(f(eta), eta)))+p*(diff(diff(g(eta), eta), eta)-R*((diff(f(eta), eta))*g(eta)-f(eta)*(diff(g(eta), eta)))+1.0*(diff(f(eta), eta))) = 0

 

(1-p)*(diff(diff(theta(eta), eta), eta))+p*(diff(diff(theta(eta), eta), eta)+10*R*f(eta)*(diff(theta(eta), eta))+.1*(diff(phi(eta), eta))*(diff(theta(eta), eta))+.1*(diff(theta(eta), eta))^2) = 0

 

(1-p)*(diff(diff(phi(eta), eta), eta)+1.000000000*(diff(diff(theta(eta), eta), eta)))+p*(diff(diff(phi(eta), eta), eta)+.5*R*f(eta)*(diff(phi(eta), eta))+1.000000000*(diff(diff(theta(eta), eta), eta))) = 0

(4)

f(eta)=sum(f[i](eta)*p^i,i=0..1);

f(eta) = f[0](eta)+f[1](eta)*p

(5)

g(eta)=sum(g[i](eta)*p^i,i=0..1);

g(eta) = g[0](eta)+g[1](eta)*p

(6)

theta(eta)=sum(theta[i](eta)*p^i,i=0..1);

theta(eta) = theta[0](eta)+theta[1](eta)*p

(7)

phi(eta)=sum(phi[i](eta)*p^i,i=0..1);

phi(eta) = phi[0](eta)+phi[1](eta)*p

(8)

FORequ1

A:=collect(expand(subs(f(eta)=f[0](eta)+f[1](eta)*p,g(eta)=g[0](eta)+g[1](eta)*p,hpm1)),p);

(-1.*R*(diff(f[1](eta), eta))*(diff(diff(f[1](eta), eta), eta))+R*f[1](eta)*(diff(diff(f[1](eta), eta), eta)))*p^3+(-1.*R*(diff(f[0](eta), eta))*(diff(diff(f[1](eta), eta), eta))-1.*R*(diff(f[1](eta), eta))*(diff(diff(f[0](eta), eta), eta))+R*f[0](eta)*(diff(diff(f[1](eta), eta), eta))+R*f[1](eta)*(diff(diff(f[0](eta), eta), eta)))*p^2+(diff(diff(diff(diff(f[1](eta), eta), eta), eta), eta)-1.0*(diff(g[1](eta), eta))-1.*R*(diff(f[0](eta), eta))*(diff(diff(f[0](eta), eta), eta))+R*f[0](eta)*(diff(diff(f[0](eta), eta), eta)))*p+diff(diff(diff(diff(f[0](eta), eta), eta), eta), eta)-1.0*(diff(g[0](eta), eta)) = 0

(9)

A1:=diff(f[0](eta),eta$4)-2*K[r]*(diff(g[0](eta),eta))=0;
A2:=diff(f[1](eta),eta$4)-2*K[r]*(diff(g[1](eta),eta))-R*(diff(f[0](eta),eta))*(diff(f[0](eta),eta$2))+R*f[0](eta)*(diff(f[0](eta),eta$2))=0;

diff(diff(diff(diff(f[0](eta), eta), eta), eta), eta)-1.0*(diff(g[0](eta), eta)) = 0

 

diff(diff(diff(diff(f[1](eta), eta), eta), eta), eta)-1.0*(diff(g[1](eta), eta))-R*(diff(f[0](eta), eta))*(diff(diff(f[0](eta), eta), eta))+R*f[0](eta)*(diff(diff(f[0](eta), eta), eta)) = 0

(10)

icsA1:=f[0](0)=0,D(f[0])(0)=1,g[0](0)=0,f[0](1)=lambda,D(f[0])(1)=0,g[0](1)=0;
icsA2:=f[1](0)=0,D(f[1])(0)=0,g[1](0)=0,f[1](1)=0,D(f[1])(1)=0,g[1](1)=0;

f[0](0) = 0, (D(f[0]))(0) = 1, g[0](0) = 0, f[0](1) = .5, (D(f[0]))(1) = 0, g[0](1) = 0

 

f[1](0) = 0, (D(f[1]))(0) = 0, g[1](0) = 0, f[1](1) = 0, (D(f[1]))(1) = 0, g[1](1) = 0

(11)

NULLFORequ2

B:=collect(expand(subs(f(eta)=f[0](eta)+f[1](eta)*p,g(eta)=g[0](eta)+g[1](eta)*p,hpm2)),p);

(-1.*R*(diff(f[1](eta), eta))*g[1](eta)+R*f[1](eta)*(diff(g[1](eta), eta)))*p^3+(-1.*R*(diff(f[0](eta), eta))*g[1](eta)-1.*R*(diff(f[1](eta), eta))*g[0](eta)+R*f[0](eta)*(diff(g[1](eta), eta))+R*f[1](eta)*(diff(g[0](eta), eta)))*p^2+(diff(diff(g[1](eta), eta), eta)+1.0*(diff(f[1](eta), eta))-1.*R*(diff(f[0](eta), eta))*g[0](eta)+R*f[0](eta)*(diff(g[0](eta), eta)))*p+diff(diff(g[0](eta), eta), eta)+1.0*(diff(f[0](eta), eta)) = 0

(12)

B1:=diff(g[0](eta),eta$2)+2*K[r]*(diff(f[0](eta),eta))=0;
B2:=diff(g[1](eta),eta$2)+2*K[r]*(diff(f[1](eta),eta))-R*(diff(f[0](eta),eta))*g[0](eta)+R*f[0](eta)*(diff(g[0](eta),eta))=0;

diff(diff(g[0](eta), eta), eta)+1.0*(diff(f[0](eta), eta)) = 0

 

diff(diff(g[1](eta), eta), eta)+1.0*(diff(f[1](eta), eta))-R*(diff(f[0](eta), eta))*g[0](eta)+R*f[0](eta)*(diff(g[0](eta), eta)) = 0

(13)

icsB1:=f[0](0)=0,D(f[0])(0)=1,g[0](0)=0,f[0](1)=lambda,D(f[0])(1)=0,g[0](1)=0;
icsB2:=f[1](0)=0,D(f[1])(0)=0,g[1](0)=0,f[1](1)=0,D(f[1])(1)=0,g[1](1)=0;

f[0](0) = 0, (D(f[0]))(0) = 1, g[0](0) = 0, f[0](1) = .5, (D(f[0]))(1) = 0, g[0](1) = 0

 

f[1](0) = 0, (D(f[1]))(0) = 0, g[1](0) = 0, f[1](1) = 0, (D(f[1]))(1) = 0, g[1](1) = 0

(14)

FORequ3

C:=collect(expand(subs(theta(eta)=theta[0](eta)+theta[1](eta)*p,phi(eta)=phi[0](eta)+phi[1](eta)*p,f(eta)=f[0](eta)+f[1](eta)*p,hpm3)),p);

(10.*R*f[1](eta)*(diff(theta[1](eta), eta))+.1*(diff(phi[1](eta), eta))*(diff(theta[1](eta), eta))+.1*(diff(theta[1](eta), eta))^2)*p^3+(10.*R*f[0](eta)*(diff(theta[1](eta), eta))+10.*R*f[1](eta)*(diff(theta[0](eta), eta))+.1*(diff(phi[0](eta), eta))*(diff(theta[1](eta), eta))+.1*(diff(phi[1](eta), eta))*(diff(theta[0](eta), eta))+.2*(diff(theta[0](eta), eta))*(diff(theta[1](eta), eta)))*p^2+(diff(diff(theta[1](eta), eta), eta)+10.*R*f[0](eta)*(diff(theta[0](eta), eta))+.1*(diff(phi[0](eta), eta))*(diff(theta[0](eta), eta))+.1*(diff(theta[0](eta), eta))^2)*p+diff(diff(theta[0](eta), eta), eta) = 0

(15)

C1:=diff(theta[0](eta),eta$2)=0;
C2:=diff(theta[1](eta), eta, eta)+Pr*R*f[0](eta)*(diff(theta[0](eta), eta))+Nb*(diff(phi[0](eta), eta))*(diff(theta[0](eta), eta))+Nt*(diff(theta[0](eta), eta))^2=0;

diff(diff(theta[0](eta), eta), eta) = 0

 

diff(diff(theta[1](eta), eta), eta)+10*R*f[0](eta)*(diff(theta[0](eta), eta))+.1*(diff(phi[0](eta), eta))*(diff(theta[0](eta), eta))+.1*(diff(theta[0](eta), eta))^2 = 0

(16)

icsC1:=theta[0](0)=1,theta[0](1)=0;
icsC2:=f[0](0)=0,D(f[0])(0)=1,f[1](1)=0,D(f[1])(1)=0,theta[1](0)=0,theta[1](1)=0,phi[0](0)=0,phi[0](1)=0;

theta[0](0) = 1, theta[0](1) = 0

 

f[0](0) = 0, (D(f[0]))(0) = 1, f[1](1) = 0, (D(f[1]))(1) = 0, theta[1](0) = 0, theta[1](1) = 0, phi[0](0) = 0, phi[0](1) = 0

(17)

FORequ4

E:=collect(expand(subs(theta(eta)=theta[0](eta)+theta[1](eta)*p,phi(eta)=phi[0](eta)+phi[1](eta)*p,f(eta)=f[0](eta)+f[1](eta)*p,hpm4)),p);

.5*R*f[1](eta)*p^3*(diff(phi[1](eta), eta))+(.5*R*f[0](eta)*(diff(phi[1](eta), eta))+.5*R*f[1](eta)*(diff(phi[0](eta), eta)))*p^2+(diff(diff(phi[1](eta), eta), eta)+1.000000000*(diff(diff(theta[1](eta), eta), eta))+.5*R*f[0](eta)*(diff(phi[0](eta), eta)))*p+diff(diff(phi[0](eta), eta), eta)+1.000000000*(diff(diff(theta[0](eta), eta), eta)) = 0

(18)

E1:=diff(phi[0](eta),eta$2)+Nt*(diff(theta[0](eta),eta$2))/Nb=0;
E2:=diff(phi[1](eta),eta$2)+Nt*(diff(theta[1](eta),eta$2))/Nb+R*Sc*f[0](eta)*(diff(phi[0](eta),eta))=0;

diff(diff(phi[0](eta), eta), eta)+1.000000000*(diff(diff(theta[0](eta), eta), eta)) = 0

 

diff(diff(phi[1](eta), eta), eta)+1.000000000*(diff(diff(theta[1](eta), eta), eta))+.5*R*f[0](eta)*(diff(phi[0](eta), eta)) = 0

(19)

icsE1:=phi[0](0)=1,phi[0](1)=0;
icsE2:=f[0](0)=0,D(f[0])(0)=1,f[1](1)=0,D(f[1])(1)=0,theta[1](0)=0,theta[1](1)=0,phi[1](0)=0,phi[1](1)=0;

phi[0](0) = 1, phi[0](1) = 0

 

f[0](0) = 0, (D(f[0]))(0) = 1, f[1](1) = 0, (D(f[1]))(1) = 0, theta[1](0) = 0, theta[1](1) = 0, phi[1](0) = 0, phi[1](1) = 0

(20)

``

NULL



Download Project.mw


Project.mw

Download Project.mw

thanks for your favorits

Hi everyone.

I'm going to solve a problem with HPM in Maple. I wrote some initial codes but now I'm confused becouse of P^0 coefficients in A1 and B1. I mean I can't reach to f0 and g0.

I upload that file. these are codes that i typed. could you please help me how can I reach to them(f0 & g0)?

http://www.filehosting.org/file/details/573095/Maple%20Project+.mw

The following code is part of my attempt to answer the recent Question about the bifurcation of the map f:= x-> exp(x^2*(a-x)). Two very weird things are happening. They can be seen by applying trace to f. The first is that the input argument to f seems to be changed to a very large integer. The second is that for some real values of a and x, I get imaginary results from this obviously real-valued function. Why are these things happening?

restart:

f:= x-> exp(x^2*(a-x)):

trace(f):

Iterate:= proc(a, x0:= 1., n:= 2000)
local A:= hfarray(1..n, [x0]), f:= subs(:-a= a, eval(:-f));          
     #evalhf(
          proc(f, A, n)
          local k;
               for k from 2 to n do A[k]:= f(A[k-1]) end do
          end proc
          (f, A, n);
     #);
     evalf[4]~(convert(A[1000..], set))
end proc:

Iterate(1.05);

{--> enter f, args = 4607182418800017408

 

HFloat(1.0512710963760241)

 

<-- exit f (now in unknown) = 4607413323290551347}
{--> enter f, args = 4607413323290551347

 

HFloat(0.9985962074909431)

 

<-- exit f (now in unknown) = 4607169774561176020}
{--> enter f, args = 4607169774561176020

 

HFloat(1.0525960836530153)

 

Warning,  computation interrupted

 

Iterate(.75);

{--> enter f, args = 4607182418800017408

 

.754589752755861+.192678397202388*I

 

<-- exit f (now in unknown) = HFloat(0.7545897527558614)+HFloat(0.19267839720238844)*I}

Error, (in unknown) unable to store 'HFloat(0.7545897527558614)+HFloat(0.19267839720238844)*I' when datatype=float[8]

 

 

 

Download bifurcation.mw

Hi everyone. This problem is driving me nuts. I'm pretty sure it's a glitch but I'm not sure how to solve it. I'm trying to do some data analysis with Maple:

(as a side note, even if I remove the for loop but don't execute the restart command the error remains, however if I get rid of the for loop and execute the restart command it is fine.)

Any help would be greatly appreciated. As it stands this is really driving me insane.

We are running Maple16 in a virtual lab setup using Citrix, when exporting to PDF and saving the file to the local machine the PDF comes out as a 0kb file and the PDF is corrupt.  Has anyone else had an issue like this before?

Hello everyone, 

I have some problems with the "isolve" command on Maple. I am trying to solve for integer a very easy system of equations. When I type the commands

 

restart; 

n := 2;
isolve({sum(a[k], k = 1 .. n)-1 = 1}, d)


I get the expected {a[1] = 2-d, a[2] = d}. However, if I add conditions a[1],a[2] >= 0, that is the commands



restart;
n := 2;
isolve({ge(a[1], 0), ge(a[2], 0), sum(a[k], k = 1 .. n)-1 = 1}, d)


I get the warning "Warning, solutions may have been lost". What am I doing wrong? Is there a way to get Maple to give me the possible values?

 

Thank you in advance,

David

Hello,

I need to prepare for a final exam for a introdutory computer science course in Maple.
My professor gives us mutliple choice questions, short answer questions and wiritng some codes.

what is the most efficient way to study for my final exam? or how should i study for an computer science exam. I am not really use to preparing for such a course. 

Are there any websites that i can practice multiple choice questions?

I would appreciate any advice.

 

Thank you very much.

@Carl Love Dear Sir i am trying to solve the system of nonlinear ODE equation with semiinfinite domain by using shooting method . but i am receiving following error 

"Error, (in isolate) cannot isolate for a function when it appears with different arguments"

how can i remove this error. i am unable to find the mistake. kindly help me 

Hi there,

 

I am trying to compute the following, and I am getting this error.

 

> A := map(convert, M, unit_free)*Unit('m'*(1/'s'^2));
(I had to put the Unit('m'*(1/'s'^2)) because the original units were kNm/s^2 (kg), and even though I simplified it, it's still using kNm/s^2, and leaves the m/s^2 for some reason when I try to remove the units. I tried simply changing the units on the original matrix, but the units menu has disappeared from the right-click menu!!)

> B := map(convert, K, unit_free);

 


Loading RealDomain;


solve;

Error, (in assuming) when calling 'Engine:-Dispatch'. Received: 'should not happen: Rename expects the input to contain unknown functions'

Why is it giving me this error? omega is an unknown variable that I am trying to solve for. I am going a modal analysis, so maybe there is a better way to find omega?

 

Any help appreciated!

 

Raquel

Maple show "

Error, (in simplify/hypergeom/baseHG) Maple was unable to allocate enough memory to complete this computation. Please see ?alloc"

after I finish the equations set and run it.

what's the reason?

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.

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