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How do I solve shooting method in Maple...

Asked by: designay 20
homework numeric differential-equations
August 02 2018
3  11

I am currently working on my Final Year project with the topic.


What Maple code can I use to compare shooting method result with the exact solutions and also plot the graph?

I have uploaded my sample questions BOUNDARY_VALUE_PROBLEMS.docx

Link to sample questions https://drive.google.com/open?id=1B9SKvcoiUw8tgFShqDwl_YHmh7If8oW0


I am grateful

how save data as table or file...

Asked by: assma 75
export
August 02 2018
0  8

how save data as table or file? such as this data aa.mw
 

 

 

Calculating a sum and subsequently taking the limi...

Asked by: digerdiga 390
sum limit
August 02 2018
1  4

I have this sum which should be equal to argument(GAMMA(I*x)) with x>0.

restart;

`assuming`([x*ln(n)-(1/2)*Pi-(sum(arctan(x/k), k = 1 .. n))], [x > 1]);

aG := `assuming`([limit(%, n = infinity)], [x > 1]);

`~`[evalf](eval([aG, argument(GAMMA(I*x))], x = 1))

 

However this limit evaluation is somehow broken in as it always gives some order symbol O(1) etc..

What is happening here?

Flatten lists with sublists...

Asked by: Annonymouse 160
list flatten
August 02 2018
0  1

Given a list with sublists e.g.

[[a,b],[[c,d,e]]]

is there a way of merging everything into a single list, for example

[a,b,c,d,e]

Why my code error when i try to execute the entire...

Asked by: dnddrgntr 5
August 02 2018
1  1

i have a problem when i try to re run my code by doing execute entire sheet, but when i first create it, it run without any errors
Thanks

using coeffs~() on a Vector...

Asked by: Annonymouse 160
vector
August 02 2018
1  1

Hi

I have a Vector of polynomials in x[1] and x[2]; and I want to use coeffs to get the coefficients of bothe elements of the Vector; using the command:

Eq2Coeffs := `~`[coeffs](%, [x[1], x[2]])

bizarely the result i get is something in terms of x[1] and x[2].

Here is the worksheet this problem emerged in, the specific command is 3.8.

wavelet codes foe solving differential equations e...

Asked by: jum 30
August 02 2018
1  0

Hi , 

I want to ask if there is any maple code of how to construct wavelet to solve fractional differential eqautions? Or any reference may be help me 

thanks 

How to address a specific case of an output by the...

Asked by: Britzel 190
label piecewise
August 02 2018
0  6

Hi there!

I like to work with output labels, since it allows me to execute a lot of code without having to make sure the respective previous calculations already ran each time I open the file.

Say my output is a list, and has label (1.3), then I can address the 2nd element of that list by (1.3)[2].

Sometimes output is organised in cases, for example when solving for the root of an equation. How can I address a specific case of that output using the output’s label?

If the case specifier is simple enough I can do that with "assuming". But when it is more complicated it is quite cumbersome to do so.

Thanks for help!

Why the frist row of my matrix is fixed, while I e...

Asked by: mehdibgh 240
matrix
August 02 2018
0  1

In the following program why the first row of Matrix P is costant, while I expect it varies?


 

``

> 

``
> 

restart
> 

with(LinearAlgebra):
> 

MCK := Matrix(1, 1, {(1, 1) = 0.1627682387e-16*mu})
> 

P := Matrix(2, 111):
> 

`ρ__∞` := 1.225:
> 

j := 1:
> 

for `U__&infin;` from 333 to 335 do `M__&infin;` := `U__&infin;`/(331.2); mu := `&rho;__&infin;`*`U__&infin;`*(`M__&infin;`^2-2)/sqrt((`M__&infin;`^2-1)^3); P[1 .. 2, j] := `<,>`(`<,>`(MCK), `<,>`(j)); j := j+1 end do:
> 

P[1, 1 .. j-1]

Vector[row]([0.1627682387e-16*mu, 0.1627682387e-16*mu, 0.1627682387e-16*mu])

 (1)
> 

``


 

Download Sooal.mw

how to break a loop and set anew iteration...

Asked by: shimaa sadk 50
loop
August 01 2018
0  4

here my problem i work on ;

i want maple to end the enternal loop if it can't solve the equation after  some iteration maple couldnt solve the equation and get stuck

 

> 

with(LinearAlgebra); with(VectorCalculus); with(Student[LinearAlgebra]); with(SignalProcessing); with(Statistics); with(stats)
> 

f[1] := n/R+sum(x[i], i = 1 .. n)-(sum((2+a[i])*x[i]*exp(R*x[i])/(exp(R*x[i])-1+Q), i = 1 .. n))
> 

f[2] := m/S+sum(y[j], j = 1 .. m)-(sum((2+b[j])*y[j]*exp(y[j]*S)/(exp(y[j]*S)-1+Q), j = 1 .. m))
> 

f[3] := (n+m+sum(a[i], i = 1 .. n)+sum(b[j], j = 1 .. m))/Q-(sum((2+a[i])/(exp(R*x[i])-1+Q), i = 1 .. n))-(sum((2+b[j])/(exp(y[j]*S)-1+Q), j = 1 .. m))
> 

NULL
> 

E1[1] := 0.5e-1
> 

E2[1] := 0.5e-1
> 

E3[1] := 0.5e-1
> 

n := 45; m := 45
> 

n := 45; m := 45
> 

a := [seq(0, i = 1 .. 21), 2, 2, 1, seq(0, i = 1 .. 21)]; b := [seq(0, i = 1 .. 21), 2, 2, 1, seq(0, i = 1 .. 21)]
> 

lambda1 := .9; lambda2 := .1; `&alpha;_&alpha;` := 5
> 

K := 1000
> 

so := 1; while so < K+1 do W := GenerateUniform(n, 0, 1); for iii to n do vv[iii] := W[iii]^(1/(iii+sum(a[jjj], jjj = n-iii+1 .. n))) end do; for sss to n do uu[sss] := 1-product(vv[n-jjj+1], jjj = 1 .. sss); x[sss] := fsolve(1-`&alpha;_&alpha;`/(exp(lambda1*t)-1+`&alpha;_&alpha;`) = uu[sss], t = 0 .. infinity) end do; U := GenerateUniform(m, 0, 1); for ii to m do v[ii] := U[ii]^(1/(ii+sum(b[jj], jj = m-ii+1 .. m))) end do; for ss to m do u[ss] := 1-product(v[m-jj+1], jj = 1 .. ss); y[ss] := fsolve(1-`&alpha;_&alpha;`/(exp(lambda2*t)-1+`&alpha;_&alpha;`) = u[ss], t = 0 .. infinity) end do; c := describe[quartile[1]]([seq(x[i], i = 1 .. n)]); cc := describe[quartile[3]]([seq(x[i], i = 1 .. n)]); L := describe[quartile[1]]([seq(y[i], i = 1 .. m)]); LL := describe[quartile[3]]([seq(y[i], i = 1 .. m)]); R[1] := fsolve(9*exp(R*c)-exp(R*cc) = 8, R = 0 .. infinity); S[1] := fsolve(9*exp(S*L)-exp(S*LL) = 8, S = 0 .. infinity); Q[1] := 3*(exp(R[1]*c)-1+(exp(S[1]*L)-1))*(1/2); for h to 40 while `and`(`and`(`and`(`and`(`and`(abs(E1[h]) > 0.5e-3, abs(E2[h]) > 0.5e-3), abs(E3[h]) > 0.5e-3), Q[h] > 2), S[h] > 0), R[h] > 0) do printlevel := 2; Q[h+1] := fsolve(eval(f[3], {R = R[h], S = S[h]}) = 0, Q = 0 .. infinity); S[h+1] := fsolve(eval(f[2], Q = Q[h+1]) = 0, S = 0 .. infinity); R[h+1] := fsolve(eval(f[1], Q = Q[h+1]) = 0, R = 0 .. infinity); if fsolve(eval(f[3], {R = R[h], S = S[h]}) = 0, Q = 0 .. infinity) = NULL then break end if; if fsolve(eval(f[2], Q = Q[h+1]) = 0, S = 0 .. infinity) = NULL then break end if; if fsolve(eval(f[1], Q = Q[h+1]) = 0, R = 0 .. infinity) = NULL then break end if; E1[h+1] := abs(R[h+1]-R[h]); E2[h+1] := abs(S[h+1]-S[h]); E3[h+1] := abs(Q[h+1]-Q[h]); KK := Matrix([[R[h]], [S[h]], [Q[h]]]) end do; A[so] := Determinant(KK[1]); B[so] := Determinant(KK[2]); C[so] := Determinant(KK[3]); so := so+1 end do

Error, cannot determine if this expression is true or false: 0 < K

  
> 

NULL
> 

NULL


 

Download Q3.mw

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Procedures, procedures...

Asked by: Inacio Aprendanet 65
August 01 2018
0  2

Hello to everyone!

 

I was trying to implement the following proc:
 

``

> 

restart; with(plots); with(plottools)
> 

"AngleSpectrum := proc( theta ) local A, B, C, a1,a2,col,k,n; n := floor(2*Pi/theta): for k from 1 to n do a1 := theta*(k-1); a2 := theta*(k); if( k mod 2 = 0) then col := COLOR(RGB,.8,.3,.5); else col := COLOR(RGB,.4,.3,.5) ; fi; A[k] := plottools[pieslice]([0,0], 1, a1..a2, color = col ): C[k] := textplot( [ evalf(1.2*cos(a2)), evalf(1.2*sin(a2)), convert(a2, string)]): od: display( seq( {A[k], C[k]}, k = 1..n), scaling=constrained); end proc:"

Error, unterminated loop

"AngleSpectrum := proc( theta ) local A, B, C, a1,a2,col,k,n; n := floor(2*Pi/theta): for k from 1 to n do a1 := theta*(k-1); a2 := theta*(k); if( k mod 2 = 0) then col := COLOR(RGB,.8,.3,.5); else col := COLOR(RGB,.4,.3,.5) ; fi; A[k] := plottools[pieslice]([0,0], 1, a1..a2, color = col ): C[k] := textplot( [ evalf(1.2*cos(a2)), evalf(1.2*sin(a2)), convert(a2, string)]): od: display( seq( {A[k], C[k]}, k = 1..n), scaling=constrained); end proc:"

  
> 

``


Can anyone help me to figure out my mistake?

Download proc.mw

Help with the loop...

Asked by: kencom1 115
loop while
August 01 2018
0  1

Good day everyone,

          I am trying to write a code for the loop of the equations below such the Theta[k] and Phi[k] start from 2 to M while F[k] starts from 4  to M.

         Anyone with good informations should please.
         Below is the link.

Thanks in anticipation

Solution_1.mw

How to write simplify(eval(…)) as composition simp...

Asked by: Britzel 190
syntax composition
August 01 2018
0  2

Hi there!

In order to keep the code more readable, and to spare myself some brackets, I am trying to use the function composition to write

simplify(eval(f(x),x=a))

as

simplify@eval(f(x),x=a))

but it doesn't work. How would I do it the right way? (I am coding in 2D math)

 

Thanks for help!

Can not open context menu...

Asked by: elen 5
solve context-menu
August 01 2018
1  5

Hello everyone! I have just started to using Maple 13. I want to solve complex eauation systems.

When I am working on Maple, If I write simple mathematical calculation and then press right click, the context menu open. However, I want to use solve command. Therefore I wrote an eauation after than press right click the context menu will not open. 

What is the reason of this problem? 

Error when create MapleSim custom component...

Asked by: HuanLuong 15
August 01 2018
1  4

Hi everyone, I need to use the integral calculation in MapleSim but there is no MapleSim Block to do it. So I create a Custom Component and using the integral calculation from Maple, the expression of the equation was done. But when I click Dimension analysis button, one error popped out as the photo. Have anyone got the same error before? How should I do to solve it? Thank you very much.

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