MaplePrimes Questions

 can you help me to solve BVP by using homotopy perturbation method
 

``

restart

with(student); -1; n := 5; 1; v := sum(y[i]*p^i, i = 0 .. n); -1; y[0] := 1; 1; D(y[0]) := gamma

5

 

1

 

gamma

(1)

for i to n do y[i] := expand(subs(coeff(diff(v, x, x)-(diff(y[0], x, x))+p*(diff(y[0], x, x)-v+cos(x)), p^i))) end do;

-1+cos(x)

 

1-2*cos(x)+cos(x)^2

 

-1+3*cos(x)-3*cos(x)^2+cos(x)^3

 

1-4*cos(x)+6*cos(x)^2-4*cos(x)^3+cos(x)^4

 

-1+5*cos(x)-10*cos(x)^2+10*cos(x)^3-5*cos(x)^4+cos(x)^5

(2)

s := simplify(sum(y[k], k = 0 .. n));

cos(x)*(cos(x)^4-4*cos(x)^3+7*cos(x)^2-6*cos(x)+3)

 

cos(x)*(cos(x)^4-4*cos(x)^3+7*cos(x)^2-6*cos(x)+3)

(3)

``

``


 

Download homotopy.mw

Hello.

When I m working on my laptop the plots wont show as it would on my stationnary machine. The surfaces is smooth without any grid and spacecurves dont display at all.

 

I have tried to uninstall and install maple without sucsess. This is maple 2016

 

Hello

My question regarding a lookup function is enclosed in the file.

lookup.mw

The Maplets, Elements, ListBox (ListBox) example given on the help page doesn't work.  I use the button to transfer the page to a worksheet window but then when I execute them I get an error.  Below is the example given on the help page.  And following that is the errors given after execution.

Is it possible to get maple to show the system of equations as output?

 

Thanks

Q1: Pascal’s Matrix of order n is given by:
Sij =(i + j)!/ i!*j!
Use Mable to produce Pascal’s Matrix of order 8.

Q2: Study the Matrix decomposition (i.e. QR, LU, and LLT), then use Maple to produce these decompositions for a random Matrix of order 6.

Q3: Write one paragraph of your own to explain Moore-Penrose Inverse of a Matrix. Use Maple to find Moore-Penrose Inverse for a random Matrix of order 8.

Q4: Use Maple to find Jordan Canonical form for a random Matrix of order 10.

Q5: Use the seq command to generate the triple [i,j,k] for all possible values for 1 ≤ i,j,k ≤ 10, then plot this triple. i.e. Use nested seq .

Q6: Let F[n] be the set:
F[n] = {p / q: 1 ≤ q ≤ n,p ≤ p ≤ q}
Use Maple to find F[6].

To keep upgrading Maple in our university we need to justify it's usage. We have an unlimited floating license. How can we track the usage of Maple by our students, faculty, etc?

f1:=(1/s^2)^N;

Maple failed to convert it into  f1:=s^(-2N);

 

I understand how Browse() works. Sometimes Maple crashes or fails for some programs. Is it possible to add print("here" ) into the the mla files in the library to identify why and where Maple fails?

 

Thanks

 

How do I simulate the follow stochastic differential equations. Thanks very much!

dx=x*(5-2*x-3*y-z)dt+5x*dB1(t);

dy=y*(4-*x-5*y-2z)dt+4y*dB2(t);

dz=z*(2-5*x-7*y-2z)dt+2z*dB3(t);

I want to plot the eigenvalues of a 4x4 matrix. I know how to determine the eigenvalues, but how do i plot them? Because i saw that plot only works with real numbers. The result is a column vector. 

Hi dears,

How can I detect two equivalent matrices? Is there any Maple command for this?

Also, Is there any command to verify that two matrices have the same Smith normalform?

Sincerely yours

I would like to return local variable y (line 4 in showstat) in the attached dummy procedure (s1) without manually adding any comment inside the procedure s1. This procedure is a simple one and easy to copy paste/or change. When we have a long procedure, it is difficult to do so. I will always know the name of the local variable I want (say, y) and/or line number in showstat

Thanks

PS, I want to get y:=array(1..,2[(1)=x,2=zz])
 

restart;

s1:=proc(n,x)
local y,xx,i,j,zz::array(1..n,1..n);
for i from 1 to n do for j from 1 to n do zz[i,j]:=x[i]*(1+x[j]^2);od:
od:
y:=array(1..2,[(1)=x, (2)=zz]):
for j from 1 to n do xx[i]:=zz[i,i]/(add(zz[i,j],j=1..n));od:
0;
end proc;

s1 := proc (n, x) local y, xx, i, j, zz::(array(1 .. n, 1 .. n)); for i to n do for j to n do zz[i, j] := x[i]*(1+x[j]^2) end do end do; y := array(1 .. 2, [1 = x, 2 = zz]); for j to n do xx[i] := zz[i, i]/add(zz[i, j], j = 1 .. n) end do; 0 end proc

(1)

showstat(s1);

 

s1 := proc(n, x)

local y, xx, i, j, zz::array(1 .. n,1 .. n);

   1   for i to n do

   2     for j to n do

   3       zz[i,j] := x[i]*(1+x[j]^2)

         end do

       end do;

   4   y := array(1 .. 2,[1 = x, 2 = zz]);

   5   for j to n do

   6     xx[i] := zz[i,i]/add(zz[i,j],j = 1 .. n)

       end do;

   7   0

end proc

 

 

x0:=Vector(2,[1,1]);

x0 := Vector(2, {(1) = 1, (2) = 1})

(2)

s1(2,x0);

0

(3)

 


 

Download showstatexample.mws

Dear All

I am trying to use differential operator two times in sucession but I am not getting desired differentiation. Please see content below:


 

with(PDEtools):

DepVars := [u(x, t), v(x, t), phi(x, t), psi(x, t)]; 1; declare(u(x, t), v(x, t), phi(x, t), psi(x, t))

[u(x, t), v(x, t), phi(x, t), psi(x, t)]

 

u(x, t)*`will now be displayed as`*u

 

v(x, t)*`will now be displayed as`*v

 

phi(x, t)*`will now be displayed as`*phi

 

psi(x, t)*`will now be displayed as`*psi

(1)

_local(I):

I := phi(x, t)*(diff(v(x, t), x)+b*(diff(u(x, t), x, x)))+psi(x, t)*(diff(u(x, t), x, x, x)+d*(diff(v(x, t), x, x)))

phi(x, t)*(diff(v(x, t), x)+b*(diff(diff(u(x, t), x), x)))+psi(x, t)*(diff(diff(diff(u(x, t), x), x), x)+d*(diff(diff(v(x, t), x), x)))

(2)

ToJet(I, DepVars)

phi*(b*u[x, x]+v[x])+psi*(d*v[x, x]+u[x, x, x])

(3)

T[1] := proc (f) options operator, arrow; diff(f, u[x]) end proc; 1; T[2] := proc (f) options operator, arrow; diff(f, u[x, x]) end proc; 1; T[3] := proc (f) options operator, arrow; diff(f, u[x, x, x]) end proc; 1; U[1] := proc (f) options operator, arrow; diff(f, v[x]) end proc; 1; U[2] := proc (f) options operator, arrow; diff(f, v[x, x]) end proc

proc (f) options operator, arrow; diff(f, u[x]) end proc

 

proc (f) options operator, arrow; diff(f, u[x, x]) end proc

 

proc (f) options operator, arrow; diff(f, u[x, x, x]) end proc

 

proc (f) options operator, arrow; diff(f, v[x]) end proc

 

proc (f) options operator, arrow; diff(f, v[x, x]) end proc

(4)

d := proc (f) options operator, arrow; diff(f, x)+u[x]*(diff(f, u))+u[x, x]*(diff(f, u[x]))+u[x, x, x]*(diff(f, u[x, x])) end proc

proc (f) options operator, arrow; diff(f, x)+u[x]*(diff(f, u))+u[x, x]*(diff(f, u[x]))+u[x, x, x]*(diff(f, u[x, x])) end proc

(5)

T[2](I)

0

(6)

Why this is giving zero result ?

If I change Ito jet notation then I get result non zero result like:

T[2](phi*(b*u[x, x]+v[x])+psi*(d*v[x, x]+u[x, x, x]))

phi*b

(7)

d(T[2](phi*(b*u[x, x]+v[x])+psi*(d*v[x, x]+u[x, x, x])))

0

(8)

I was expecting this to be "phi[x]*b, "but instead I am getting zero result.``


 

Download operator_for_differentiation.mw

I'm sorry if this sounds like a noob question. I am trying to make a matrix from a table, something like Gauss-Jordan Elimination tutor.

For example

maplet1 := Maplet([BoxCell(Table([A, B], [[1, 2], [3, 4]]), 'as_needed'), Button("OK", Shutdown())]);

How do I turn it to 2x2 matrix?Any help appreciated

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