Maple 12 Questions and Posts

These are Posts and Questions associated with the product, Maple 12

i have this sequence :f:=n->n/n+1
       

> f1:=seq(f(n), n = 0 .. 10);
                       f1:= 0,1/2,3/4,4/5,5/6,6/7,7/8,8/9,10/11

i want to create these sequences by using f :

1) 0,2/3,4/5,6/7,8/9,...

2)2/3,9/10,16/17,..

3) 1/2^2,3^2/4^2,5^2/6^2,7^2/8^2

4)0,3/4,8/9,24/25,35/36
        can anyone help me ?              

I have a function which describes the complex reflection coefficient of a structure with respect to frequency.  One or more variables may control the function, and I want to find the set of variables which yield the lowest maxima in frequency response, over a given range of frequencies.

For a simple example relying only on a single variable "Z", it would be something like this:

NLPSolve(

NLPSolve(abs(Gamma),f=f1..f2,maximize),

Z=Z[1]..Z[N],

initialpoint = [Z=Z[2]]

);

I suspect I am having two problems with the above:

1.  Without some numeric starting point for Z, the nested NLPSolve(Gamma,f=f1..f2,maximize), Gamma is failing to resolve to a maxima in the range f = f1..f2.  Testing NLPSolve(subs(Z=1,abs(Gamma)),f=0..1,maximize); works just fine, but not without fixing Z to some undesired point.

2.  Maple seems to be unhappy about the inclusion of abs(), stating "abs is not differentiable at non-real arguments".  However, a test of another simpler complex function did not bring about the same complaint, so perhaps this is a misleading error due to the poor structure of my command.

Help!

Thank you.

A system of differential equations

But solution I want to express in terms of other specified function

How to dsolve to get a solution that in terms of a list of specified function? For example in terms of sin , cos , Bessel etc ?

Sol := [a(t) = sin(t) + cos(t) , b(t)= sin(t) ....]

I wish to solve a diffrential equation of the type:

u(du/dx)^2=a_1*u^4+a_2*u^3+a_3*u^2+a_4*u+a_5

where coefficients a_1,a_2,...are constants with respect to x.

I am trying to convert this equation in normal Weirstrass Form.

Can someone please help

How can maple be trusted app when window 10 device guard enabled?

F(n,n+1),2) = F(Product(x, k=1..n), 2)

how to solve function F?

Update
 

Above equation is wrong, below is newly updated 

Expect F is product operator

F(2,3) + 2 = F(2,4)

F(3,4) + 3 = F(3,5)

solve([ F(1,2)+1=F(1,3), F(n,n+1) + n = F(n,n+2), F(n,n+1)= F(summation(k,k=1..n),2)],F) assuming n > 0

Expect F is new operator
solve([ F(1,2)*1=F(1,3), n*F(n,n+1) = F(n,n+2), F(n,n+1)= F(product(k,k=1..n),2)],F) assuming n > 0

Dear all
Using cubic spline interpolation to interpolate a given function I get  
the follwoing error
Warning, solving for expressions other than names or functions is not recommended.
Error, (in solve) list of unknowns contains repeated elements: [1, 0]

and  why the  spline funciton obtained by this code is different to the one given by Maple's built in package.

inter.mw

Thank you for any help 

Dear all

I solve a given pde with some conditions given, but I get 

unable to handle PDE problem subject to boundary conditions 

solution_pdes.mw

many thanks for your help

 

 

Dear all

for a fixed x positive, I would like to find an asymptotic expansion of the following integral when n goes to infinity. 

int(exp(-n*(x*cosh(t)+t)), t = 0 .. infinity)

Maybe we can define 
f:=n->int(exp(-n*(x*cosh(t)+t)), t = 0 .. infinity);
Then 

asympt(f(n), n,2)
But doesn't work

Many thanks for your help 

 

Dear all

I have a nonlinear PDE, I use a transformation depend on some paramaters I would like to find the scalling parameters so that the pde is invariant under the proposed transformation.

PDes_invariant_under_transformation.mw

Thak you for your help 

 

Would like to export a list into a text file

when I tried , it show ... 1234 items... , can not export a whole list into text file.

[[[0,0,0,0]], [[0,0,0,0]], .....]
thousands of [[...]] elements

 

Dear all

I would like to solve a fourth order PDEs, using fourier transform. 

How can I apply fourier transform to get solution of my problem

Fourier_transform.mw

Thank you 

Dear all

I compute the solution of a system of ordinary differential equaiton using Picard iteration. I have the following error:

Error, invalid input: f uses a 2nd argument, y, which is missing

My code 

Picard_iteration.mw

Thank you for any help 

 

[[1,1,["ab","xy"]], [0,1,["xy"]]]
 

how to sort by first number , second number , and list of string ?

how to count and group by third list of strings having first two number 0,0 or 0,1 or 1,0 or 1,1 

for example 

["xy"] at most count 4  , at least count 1

would like to find which is [1,1,... ] and only count 1

 

second has rsolve solution

compare original sequence

accsum(ListTools[Reverse]([seq(patterngroup[k], k=(mm)..(mm+lengthofsequence))])),

with rsolve solution , it start from third number wrong, some number are wrong but correct at next number, 

but i just want to guess next number is 1 or 2

[seq(subs(k=kk, sol), kk=0..(lengthofsequence+1))],

with(SumTools):
with(gfun):
accsum := proc(xx)
local result,mm:
result := []:
for mm from 1 to nops(xx) do
temp := Summation(xx[k], k = 1 .. mm):
result := [op(result), temp]:
od:
return result:
end proc:


patterngroup := [2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1]: # left is latest, 2,1,1..
lengthofsequence := 5:
for mm from 1 to 12 do
if guessgf(accsum(Reverse([seq(patterngroup[k], k=(mm)..(mm+lengthofsequence))])), x) = FAIL then
print(patterngroup[mm]):
else
sol := rsolve(listtorec(accsum(ListTools[Reverse]([seq(patterngroup[k], k=(mm)..(mm+lengthofsequence))])), u(n))[1], u(k)):
acxxc := accsum(ListTools[Reverse]([seq(patterngroup[k], k=(mm)..(mm+lengthofsequence))])):
olist := [seq(patterngroup[k], k=(mm)..(mm+5))]:
#start from 0
print(patterngroup[mm], olist, accsum(ListTools[Reverse]([seq(patterngroup[k], k=(mm)..(mm+lengthofsequence))])), [seq(subs(k=kk, sol), kk=0..(lengthofsequence+1))], sol, subs(k=(lengthofsequence+1), sol), subs(k=(lengthofsequence+1), sol)-acxxc[nops(acxxc)]):
end if:
od:
 

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