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First order frequency response, no plot possible....

Asked by: Jogibaer 5
April 16 2017
1  1

Hi guys,

I've had only a little experience with Maple, but I decided to use it for preliminary frequecy response calculations. The funny thing is, I have already the solution in some way, but I'm too stupid to get it working. I can't see the mistake, however, it should have something to do with the H_n(f) function and the other normalized functions.

NASA has published a nice paper which explains the calculations, however, they have used MathCAD. Anyway, I don't think this should be a problem. Here is the documentation: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070016024.pdf 

The error message is for example for the H_n(f) function:

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

 

Please help me.

Maple file: calculations.mw

how to output all possible inequalities solutions?...

Asked by: LeeHoYeung 535
optimization
April 15 2017
0  1

i use optimization package with constraint hello >= 0

Minimize(xx=0, {hello >= 0})

but solution only return the case when hello = 0

how about hello > 0?

i would like to find all possible set of solutions using this constraint

do i need to set upper bound, such as {hello <= 7, hello >=0}

can it return solution when hello = 1.1, 1.2, ...2, 2.1, 2.2, 2.3, ....7

Parabolic PDE ...

Asked by: Melvin Brown 124
pde numeric pdsolve
April 14 2017
0  0

I am looking for a numerical solver for a parabolic PDE (up to 2nd order derivatives but no mixed ones) on the spatio-temporal domain [X x Y x T], either as an external package or as MAPLE code.  

I have coded the method of lines on the domain [X x T] and indeed also used pdsolve as a check for that case. However, pdsolve (numerical) cannot solve the PDEs on the domain [X x Y x T].  The run times and memory requirements for the latter case would of course be significantly greater.  

I am about to code up the method of lines (in MAPLE) on the domain [X x Y x T], but am wondering whether there exist external FORTRAN or C code packages that would be faster if called up in MAPLE and whose results would then be post-pocessed in MAPLE.

Does anyone have any suggestions?

MRB

how i can solve following equation?...

Asked by: 9009134 110
solve pdsolve
April 14 2017
1  0

 

hi--how i can solve following equation?

thanks

 

Eq.mw


Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Eq.mw .
 

Download Eq.mw

 

My Maple implementation of “Optimal Taxation Model...

Asked by: Leap 0
integral multivariate-calculus lagrange-multipliers
April 14 2017
0  0

I've implemented the optimal taxation model proposed in this paper using Maple.

But it never stops running and get stuck in the last line for integral computation. Any idea of what's wrong with that?

This is the last line:

Here is the full code.

PDE numeric BVP how to solve and guess initial con...

Asked by: faisal 15
pde numeric pdsolve
April 13 2017
0  1


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

How to view the source code for a created .mv file...

Asked by: ykteoh 5
worksheet export
April 07 2017
1  4

How to view the source code for a created .mv file in Maple?

I need help for these examples...

Asked by: kmasoud7787 10
homework
April 05 2017
1  0

Need numerical solution of PDE...

Asked by: Muhammad Usman 245
numeric pdsolve
April 05 2017
0  3

Dears 

Hope you would be fine. I want to solve the following PDEs by numerically for v[nf]=alpha[nf]=Ec=mu[nf]=C=1 and Pr=6.2

Eq1 := diff(u(x, t), t) = v[nf]*(diff(u(x, t), x, x));

Eq2 := diff(u(x, t), t) = alpha[nf]*(diff(theta(x, t), x, x))/Pr+Ec*mu[nf]*C*(diff(u(x, t), x))^2;

ICs := u(x, 0) = 0, theta(x, 0);

BCs := u(0, t) = 1, theta(0, t) = 1, u(10, t) = 0, theta(10, t) = 0;

and find the values of (diff(u(0, t), x))/(1-phi)^2.5 for different values of phi. Thanks in advace 

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

How can I wite a Maple code that can handle severa...

Asked by: owoicholohi 5
do-loop
April 04 2017
1  2

Please can someone help me with looping involving 4 variables such as S1 S2 S3 S4 from a series

Sn+1 =f(f-a)+u+Vn+w

Vn+1 =wc+f a-An+ u  if An = Un+Vn

How to create a hyperplane which perpendicular to ...

Asked by: LeeHoYeung 535
April 04 2017
0  0

How to create a hyperplane which perpendicular to groebner basis

Error, (in Groebner:-NormalSet) The case of non-ze...

Asked by: LeeHoYeung 535
groebner
April 04 2017
0  3
tord := plex(x, y, z);
G := Basis([hello1, hello2, hello3], tord);
ns, rv := NormalSet(G, tord);
Error, (in Groebner:-NormalSet) The case of non-zero-dimensional varieties is not handled
is this error due to version of maple?
which version do not have this error?
 

How to solve delay differential equation by method...

Asked by: rkdevkate 5
dsolve dde
April 04 2017
1  2

How to solve delay differential equation by method of steps in MAPLE software. 

How can I generate series of variables using Maple...

Asked by: Elisha 50
do-loop
April 04 2017
0  0


 

> 

restart
> 

with(student)
> 

``
> 

G := S(t)*L(t)

S(t)*L(t)

 (1)
> 

m := 10
> 

S[lambda] := sum(S[b]*lambda^b, b = 0 .. m); L[lambda] := sum(L[b]*lambda^b, b = 0 .. m); G[lambda] := subs(S(t) = S[lambda], G); G[lambda] := subs(L(t) = L[lambda], G[lambda]); G := G[lambda]; s := expand(G, lambda); ft := unapply(s, lambda); for i from 0 while i <= m do A1[i] := ((D@@i)(ft))(0)/factorial(i); print(A[i] = A1[i]) end do

A[0] = S[0]*L[0]

  

A[1] = L[0]*S[1]+L[1]*S[0]

  

A[2] = L[0]*S[2]+L[1]*S[1]+L[2]*S[0]

  

A[3] = L[0]*S[3]+L[1]*S[2]+L[2]*S[1]+L[3]*S[0]

  

A[4] = L[0]*S[4]+L[1]*S[3]+L[2]*S[2]+L[3]*S[1]+L[4]*S[0]

  

A[5] = L[0]*S[5]+L[1]*S[4]+L[2]*S[3]+L[3]*S[2]+L[4]*S[1]+L[5]*S[0]

  

A[6] = L[0]*S[6]+L[1]*S[5]+L[2]*S[4]+L[3]*S[3]+L[4]*S[2]+L[5]*S[1]+L[6]*S[0]

  

A[7] = S[5]*L[2]+S[2]*L[5]+S[1]*L[6]+S[0]*L[7]+S[4]*L[3]+S[3]*L[4]+S[6]*L[1]+S[7]*L[0]

  

A[8] = S[2]*L[6]+S[0]*L[8]+S[8]*L[0]+S[4]*L[4]+S[1]*L[7]+S[3]*L[5]+S[6]*L[2]+S[5]*L[3]+S[7]*L[1]

  

A[9] = S[6]*L[3]+S[9]*L[0]+S[4]*L[5]+S[2]*L[7]+S[3]*L[6]+S[8]*L[1]+S[0]*L[9]+S[1]*L[8]+S[7]*L[2]+S[5]*L[4]

  

A[10] = S[0]*L[10]+S[10]*L[0]+S[1]*L[9]+S[6]*L[4]+S[7]*L[3]+S[3]*L[7]+S[2]*L[8]+S[4]*L[6]+S[9]*L[1]+S[5]*L[5]+S[8]*L[2]

 (2)

s[n+1] := (1-f)*alpha*(int(v__n, t = 0 .. t))-beta*c*(int(A__n, t = 0 .. t))-(`&theta;__1`+a+Pi)*(int(s__n, t = 0 .. t))

v[n+1] := `&theta;__1`*(int(s__n, t = 0 .. t))-((1-f)*alpha+f*`&theta;__2`+a+Pi)*(int(v__n, t = 0 .. t))

e[n+1] := `&beta;c`*(int(A__n, t = 0 .. t))-(delta+a+Pi)*(int(e__n, t = 0 .. t))

i[n+1] := delta*(int(e__n, t = 0 .. t))-(eta+a+Pi)*(int(i__n, t = 0 .. t))

r[n+1] := eta*(int(i__n, t = 0 .. t))+`f&theta;__2`*(int(v__n, t = 0 .. t))-(a+Pi)*(int(r__n, t = 0 .. t))

for n from 0 to 4 do end do

``

(1-f)*alpha*v__n*t-beta*c*s__0*i__0*t-(`&theta;__1`+a+Pi)*s__n*t

 (3)

"for n:=0, n=1, n=2, n=3, n=4: `s__1, ``s__2__`, `s__3, ``s__4`, `i__1`, `i__2, ``i__3`, `i__4`, `r__1`, `r__2`, `r__3, ``r__4`:"

Error, unterminated for loop

"for n:=0, n=1, n=2, n=3, n=4: `s__1, ` `s__2__`, `s__3, __3__, s__4`, `i__1__`, `i__2, ` `i__3`, `i__4`, `r__1`, `r__2`, `r__3, ` `r__4`:"

  

"and s(t)=`s__1_`+`s__2 __`+ `s__3, `+`s__4`,"

i(t) = i__1+`i__2, `+i__3+i__4, r(t) = r__1+r__2+r__3_+r__4

"but A[n]:=(1)/(n!) [((&DifferentialD;)^(n))/(&DifferentialD; lambda^(n)) ((&sum;)`s__k`lambda^(k))((&sum;)`i__k`lambda^(k)) ]() ? ()|() ? (lambda=0)"

Error, missing numerator

Typesetting:-mambiguous(Typesetting:-mrow(Typesetting:-mi("but", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("&InvisibleTimes;", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-msub(Typesetting:-mi("A", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mi("n", fontstyle = "italic", mathcolor = "#c800c8", mathvariant = "italic", placeholder = "true"), subscriptshift = "0"), Typesetting:-mo("&Assign;", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mfrac(Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mi("n", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("&excl;", accent = "false", fence = "false", largeop = "false", lspace = "0.1111111em", mathvariant = "normal", movablelimits = "false", rspace = "0.1111111em", separator = "false", stretchy = "false", symmetric = "false")), bevelled = "false", denomalign = "center", linethickness = "1", numalign = "center"), Typesetting:-mo("&InvisibleTimes;", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfrac(Typesetting:-msup(Typesetting:-mo("&DifferentialD;", accent = "unset", fence = "unset", largeop = "unset", lspace = "0.0em", mathvariant = "normal", movablelimits = "unset", rspace = "0.0em", separator = "unset", stretchy = "unset", symmetric = "unset"), Typesetting:-mi("n", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0"), Typesetting:-mrow(Typesetting:-mo("&DifferentialD;", accent = "unset", fence = "unset", largeop = "unset", lspace = "0.0em", mathvariant = "normal", movablelimits = "unset", rspace = "0.0em", separator = "unset", stretchy = "unset", symmetric = "unset"), Typesetting:-mo("&InvisibleTimes;", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-msup(Typesetting:-mi("&lambda;", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mi("n", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0")), bevelled = "false", denomalign = "center", linethickness = "1", numalign = "center"), Typesetting:-mo("&InvisibleTimes;", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-munderover(Typesetting:-mo("&sum;", accent = "unset", fence = "unset", largeop = "true", lspace = "0.0em", mathvariant = "normal", movablelimits = "true", rspace = "0.1666667em", separator = "unset", stretchy = "true", symmetric = "unset"), Typesetting:-mrow(Typesetting:-mi("k", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("&equals;", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("0", mathvariant = "normal")), Typesetting:-mn("4", mathvariant = "normal"), accent = "false", accentunder = "false"), Typesetting:-mi("`s__k`"), Typesetting:-msup(Typesetting:-mi("&lambda;", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mi("k", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-munderover(Typesetting:-mo("&sum;", accent = "unset", fence = "unset", largeop = "true", lspace = "0.0em", mathvariant = "normal", movablelimits = "true", rspace = "0.1666667em", separator = "unset", stretchy = "true", symmetric = "unset"), Typesetting:-mrow(Typesetting:-mi("k", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("&equals;", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("0", mathvariant = "normal")), Typesetting:-mn("4", mathvariant = "normal"), accent = "false", accentunder = "false"), Typesetting:-mi("`i__k`"), Typesetting:-msup(Typesetting:-mi("&lambda;", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mi("k", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0")), mathvariant = "normal"), Typesetting:-mo("&InvisibleTimes;", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false")), open = "&lsqb;", close = "&rsqb;", mathvariant = "normal"), Typesetting:-mfrac(Typesetting:-mambiguous(Typesetting:-merror("?"), Typesetting:-merror("missing numerator")), Typesetting:-mphantom(Typesetting:-mrow(Typesetting:-mi("x", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("&equals;", accent = "unset", fence = "unset", largeop = "unset", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "unset", rspace = "0.2777778em", separator = "unset", stretchy = "unset", symmetric = "unset"), Typesetting:-mi("a", fontstyle = "italic", mathvariant = "italic")), constraints = "height-only"), bevelled = "false", denomalign = "center", linethickness = "0", numalign = "center"), Typesetting:-mo("&verbar;", accent = "unset", fence = "unset", largeop = "unset", lspace = "0.1111111em", mathvariant = "normal", movablelimits = "unset", rspace = "0.1111111em", separator = "unset", stretchy = "true", symmetric = "unset"), Typesetting:-mfrac(Typesetting:-mphantom(Typesetting:-mi("f(x)", fontstyle = "italic", mathvariant = "italic"), constraints = "height-only"), Typesetting:-mrow(Typesetting:-mi("&lambda;", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mo("&equals;", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("0", mathvariant = "normal")), bevelled = "false", denomalign = "center", linethickness = "0", numalign = "center")))

  

NULLI have tried to do the above but got the error messages. I tried changing the L in that computation above to i to enable me get the desired result but i couldn't.

> Please how can I generate the values S1,S2,S3,S4; i1,i2,i3,i4 and r1,r2,r3,r4 and finally do

S(t)=S1 + S2 + S3 + S4; i(t)= i1+i2+i3+i4 ; and r(t)=r1,r2,r3,r4  using Maple?

> 

NULL
> 

> 

> 

``
> 

``


 

Download Adomian.Elisha2.mw

How to plot a prettier bifurcation diagram using M...

Asked by: ZWang 25
imagetools iterative-map
April 04 2017
0  5

Dear All,

The following code plots the bifurcation diagram for a three-dimensional continuous dynamical system as a variable Re varies. However, the resulting plot (by pointplot command) is rather ugly, comparing with other bifurcation diagrams, see attached. Could anyone point me out how to improve its looking?

``

> 

restart:
with(plots): with(DEtools): with(plottools):with(LinearAlgebra):
doSol:=proc( R )
             local t_start:=2500,
                   t_end:=5000,
                   b:=-3,
                   c:=3,
                   v1:=1,
                   f:=-4,
                   v2:=2.0,
                   omega:=0.1*sqrt(R),
                   epsilon:=evalf(1/R),
                   k:=0.1,
                   kH:=(c+1)/(b-1),
                   sys, evs, w, M, T, i, tt, solA, N_alpha,
                   r_center, z_center, Zshift, alpha, alpha1,
                   alpha2, del_alpha, m, Z, Rshift, RR;
             sys:=diff(u1(t),t)=v1*u1(t)-(omega+k*u2(t)^2)*u2(t)-(u1(t)^2+u2(t)^2-b*z(t)^2)*u1(t),
                  diff(u2(t),t)=(omega+k*u1(t)^2)*u1(t)+v1*u2(t)-(u1(t)^2+u2(t)^2-b*z(t)^2)*u2(t),
                  diff(z(t),t)=z(t)*(kH*v1+c*u1(t)^2+c*u2(t)^2+z(t)^2)+epsilon*z(t)*(v2+f*z(t)^4):
             solA:=dsolve({sys, u1(0)=0.6, u2(0)=0.6, z(0)=0.1},
                          {u1(t),u2(t),z(t)},
                          numeric, method=rkf45, maxfun=10^7,
                          events=[[[u1(t)=0, u2(t)>0], halt]]
                         );
             evs:=Array():
             evs(1,1..4):=Array([t,u1(t),u2(t),z(t)]);
             interface(warnlevel=0):

             for i from 2 do
                 w:=solA(t_end):
                 if   rhs(w[1])<t_end
                 then evs(i,1..4):=Array(map(rhs, w));
                      solA(eventclear);
                 else break;
                 fi
             od:

             interface(warnlevel=3):
             M:=DeleteRow(convert(evs,matrix),1):

             T:=M[..,1]:

             for i from 1 do
                 tt:=T[i]:
                 if   tt>=t_start
                 then break;
                 end if;
             end do:

             RR:=M[i..,3]: Z:=M[i..,4]:

             N_alpha:=numelems(RR):

             r_center:=add(RR[i],i=1..N_alpha)/N_alpha:
             z_center:=add(Z[i],i=1..N_alpha)/N_alpha:

             Zshift:=Z-~r_center: Rshift:=RR-~z_center:

             alpha:=(arctan~(Zshift/~Rshift)+(Pi/2)*sign~(Rshift))/~(2*Pi)+~0.5:

             return alpha;
  end proc:
> 

i_start:=125: i_end:=250: i_delta:=0.1:

M:=[seq( [j, doSol(j)], j=i_start..i_end, i_delta)]:
> 

S:=seq([Vector(numelems(M[i,2]),fill=M[i,1]),M[i,2]], i=1..numelems(M),1):
display(seq( pointplot(S[i],
             symbolsize=1,
             symbol=point) ,
             i=1..numelems(M)),
             axes=boxed,
             view=[i_start..i_end,0..1],
             size=[650,400],
             axesfont= ["TimesNewRoman", 16],
             labels=["Re",phi[n]],
             labelfont = ["TimesNewRoman", 16],
             labeldirections=[horizontal, vertical]);

``


 

Bifurcation_diagram.mw

Thank you.

Very kind wishes,

Wang Zhe

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