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differential quadrature method stuck at rk4 method...

Asked by: Khair Muhammad Saraz 40
procedure loop homework
May 20 2024
1  30

im trying to write differential quadrature method i have successfully  generated system of equations using code but now im stuck with rk4 method to solve these equation in a loop kindly give me suggestions or modify the code

> 

restart
> 

with(orthopoly)
> 

N := 5

5

 (1)
> 

P := proc (n, x) options operator, arrow; orthopoly[P](n, 2*x-1) end proc
> 

P_N := simplify(P(N, x))

252*x^5-630*x^4+560*x^3-210*x^2+30*x-1

 (2)
> 

localroots := fsolve(P_N = 0, x, complex)

HFloat(0.04691007703066799), HFloat(0.23076534494715836), HFloat(0.4999999999999997), HFloat(0.7692346550528439), HFloat(0.9530899229693298)

 (3)
> 

for i to N do assign(x[i] = localroots[i]) end do
> 

PRime := diff(P_N, x)

1260*x^4-2520*x^3+1680*x^2-420*x+30

 (4)
> 

for i to N do for j to N do if i <> j then a[i, j] := (eval(PRime, x = x[i]))/((x[i]-x[j])*(eval(PRime, x = x[j]))) else a[i, j] := (1-2*x[i])/(2*x[i]*(x[i]-1)) end if end do end do
> 

u := proc (i) local u_x, expr, j; u_x := add(a[i, j]*u[j], j = 1 .. N); expr := -u[i]*u_x+x[i]; expr end proc; odes := [seq(u(i, [seq(u[j], j = 1 .. N)]), i = 1 .. N)]; for i to N do assign(o[i] = odes[i]) end do; for i to N do printf("u_%d = %s\n", i, convert(u(i), string)) end do

u_1 = -u[1]*(-10.1340811913091*u[1]+15.4039041703445*u[2]-8.08708750877537*u[3]+3.92079823166652*u[4]-1.10353370192667*u[5])+.046910077030668
u_2 = -u[2]*(-1.92051204726391*u[1]-1.51670643433575*u[2]+4.80550130432862*u[3]-1.85711605328765*u[4]+.488833230558754*u[5])+.230765344947158
u_3 = -u[3]*(.602336319455661*u[1]-2.87077648466948*u[2]-1.11022302462516e-015*u[3]+2.87077648466942*u[4]-.602336319455684*u[5])+.5
u_4 = -u[4]*(-.488833230558737*u[1]+1.85711605328767*u[2]-4.8055013043286*u[3]+1.51670643433578*u[4]+1.92051204726404*u[5])+.769234655052844
u_5 = -u[5]*(1.1035337019266*u[1]-3.92079823166643*u[2]+8.08708750877511*u[3]-15.4039041703442*u[4]+10.1340811913086*u[5])+.95308992296933

  
> 

initial_conditions := [0.1e-1, 0.2e-1, 0.3e-1, 0.4e-1, 0.5e-1]
> 

for i to N do printf("Initial condition for u_%d: u_%d(0) = %f\n", i, i, initial_conditions[i]) end do

Initial condition for u_1: u_1(0) = 0.010000
Initial condition for u_2: u_2(0) = 0.020000
Initial condition for u_3: u_3(0) = 0.030000
Initial condition for u_4: u_4(0) = 0.040000
Initial condition for u_5: u_5(0) = 0.050000

  
> 

dt := .1
> 

tf := 1
> 

"local o_old; o_old := Vector(n); #` Loop to initialize o[i]old values` for i from 1 to n do o_old[i] := initial_conditions[i]; printf("Initial condition for u_%d: u_%d(0) = %f\\n", i, i, initial_conditions[i]); end do: time := t0; while time < tf do for i from 1 to n do k[1, i] := dt * o[i](time,o_old[i]); for i from 1 to n do k[2,i]:=dt*o[i](time + dt/(2), o_old[i]+ (k[1, i])/(2)); end do: for i from 1 to n do k[3,i]:=dt*o[i](time+ o_old[i]+ ( k[1, i])/(2)); end do: for i from 1 to n do k[4,i]:=dt*o[i](time+dt,o_old[i]+k[1,i]); end do: for i from 1 to n do 0 _new[i]:=o_old[i]+(k[1,i]+2 *k[2,i]+2*k[3,i]+k[4,i]); end do: time := time + dt; end do; "

Error, illegal use of an object as a name

"local o_old; o_old := Vector(n); #` Loop to initialize o[i]old values` for i from 1 to n do o_old[i] := initial_conditions[i]; printf("Initial condition for u_%d: u_%d(0) = %f\\n", i, i, initial_conditions[i]); end do: time := t0; while time < tf do for i from 1 to n do k[1, i] := dt * o[i](time,o_old[i]); end do: for i from 1 to n do k[2,i]:=dt*o[i](time + dt/2, o_old[i]+ (k[1, i])/2); end do: for i from 1 to n do k[3,i]:=dt*o[i](time+ o_old[i]+ ( k[1, i])/2); end do: for i from 1 to n do k[4,i]:=dt*o[i](time+dt,o_old[i]+k[1,i]); end do: for i from 1 to n do 0 _new[i]:=o_old[i]+(k[1,i]+2 *k[2,i]+2*k[3,i]+k[4,i]); end do: time := time + dt; end do; "

  
 

NULL

Download dq_code.mw

Multiplaction "dot" is way too small - causes erro...

Asked by: segfault 145
multiplication
May 16 2024
1  8

Multiplaction "dot" in Maple 2022 is way too small - causes errors.

e.g. two variables multiplied s*m ends up being sm a new variable as I cannot really see that there is a missing multiplication operator between the variables. This causes huge unnecessary errors.

Maple 9.x e.g had nice clear and big operators and this kind of error was avoided.

How can I undo this unfortunate regression in Maple 2022 to increase the size of multiplication operator and other operators, so that they actually becom visible and not just a little dot almost a pixel in size.

If I was a falcon (20x20)^infinity then this would have been ok, but I am not, I am human.

So how do I change this unfortunate regression so that these errors can be avoided.?

Only ten files listed in the recents list...

Asked by: segfault 145
history gui
May 15 2024
1  6

Why does Maple 2022 still have only a history of ten files in the Recents ?

It makes it very difficult to search for files you opened but only realised later you need, but then it is long out of the silly 10 history list.

Isnt there a way to make a perpetual list so that all files opened are saved chronologiacally against date, or... at least be able to increase the silly 10 recent files to something like 30

Thanks

Procedure called in another procedure...

Asked by: Dkunb 70
parameters procedure
May 14 2024
1  1

In my code, why  does InitState(5,5) return only one element of the vector while Coherent(5) returns 5 elements of the vector?

> 

restart;
> 

with(LinearAlgebra):
> 

 

> 

Coherent := proc({zeta:=1,phi:=Pi/2},n_max) local alpha,i,ICs:
 #alpha := sqrt(zeta)*exp(I*phi):
 ICs := Vector(n_max,i->evalc(evalf(exp(-zeta/2)/sqrt((i-1)!))*(sqrt(zeta)*exp(I*phi))^(i-1)),datatype=complex[8]);
end proc:

Projectile := proc({L:=1,sigma:=0.01,beta:=0.02,k0:=-5*Pi},n_max) local x0,g,c,v,ICs,j:
  x0 := evalf(beta*L);
  g := unapply(exp(-(x-x0)^2/2/sigma^2),x);
  c := evalf(int(g(x)^2,x=-L/2..L/2,numeric=true));
 
  v:=Vector(n_max,datatype=complex[8]);

  for j from 1 to n_max do:
     if (is(j,odd)) then  v[j]:= evalc[8](evalf(Int(cos(Pi*j*x/L)*g(x)*cos(k0*x),x=-L/2..L/2,method=_d01akc))+ I*evalf(Int(cos(Pi*j*x/L)*g(x)*sin(k0*x),x=-L/2..L/2,method=_d01akc)));
      else v[j]:= evalc[8](evalf(Int(sin(Pi*j*x/L)*g(x)*cos(k0*x),x=-L/2..L/2,method=_d01akc))+ I*evalf(Int(sin(Pi*j*x/L)*g(x)*sin(k0*x),x=-L/2..L/2,method=_d01akc)));
     end if:
  end do:

 ICs :=evalf[8](sqrt(2/L*c))*v;
end proc:

InitState := proc({zeta:=1,phi:=Pi/2,L:=1,sigma:=0.01,beta:=0.02,k0:=-5*Pi},d1,d2) local Z0:
z1 := Coherent(zeta,phi,d1);
#Z0:= MatrixMatrixMultiply(Coherent(zeta,phi,d1),Transpose(Projectile(L,sigma,beta,k0,d2))):
end proc:

Warning, (in InitState) `z1` is implicitly declared local

  
> 

InitState(5,5); Coherent(5);

Vector(1, {(1) = .6065306597+0.*I})

  

Vector[column](%id = 36893490076814315516)

 (1)
 

 

Download test3.mw

integration in if-statement...

Asked by: Dkunb 70
performance integration syntax
May 13 2024
0  3

How can I get the evaluation of integration inside if-statement?

Thanks for your help in advance,

> 

restart;
> 

#L:=1:sigma:=0.01:beta:=0.2:k0:=-100:
> 

#For Free particle
Projectile := proc({L:=1,sigma:=0.01,beta:=0.2,k0:=-100},n_max) local x0,g,c:
 x0:= beta*L;
 g := unapply(exp(-(x-x0)^2/2/sigma^2),x);
 #c := int(g(x)^2,x=-L/2..L/2,numeric=true);
 ub := (L/2-x0)/sqrt(2)/sigma;
 lb := (-L/2-x0)/sqrt(2)/sigma;
 a := Pi*sqrt(2)*sigma/L;
 b := sqrt(2)*k0*sigma;
 c := Pi*x/L;
 d := k0*x0;
 eq1 := [cos(a*n*z)*cos(b*z)/e^(z^2),cos(a*n*z)*sin(b*z)/e^(z^2),sin(a*n*z)*cos(b*z)/e^(z^2),sin(a*n*z)*sin(b*z)/e^(z^2)];
 eq1 := map(f->unapply(f,n,z),eq1);
 eq2 := [cos(n*c)*cos(d),cos(n*c)*sin(d),sin(n*c)*cos(d),sin(n*c)*sin(d)];
 eq2 := map(f->unapply(f,n,z),eq2);

 for j from 1 to n_max do:
   if (is(j,odd)) then eq11 := int(eq1[1](j,z),z=lb..ub,numeric=true);
   else 0;
   end if;
 end do:

end proc:
> 

 

Warning, (in Projectile) `ub` is implicitly declared local

  

Warning, (in Projectile) `lb` is implicitly declared local

  

Warning, (in Projectile) `a` is implicitly declared local

  

Warning, (in Projectile) `b` is implicitly declared local

  

Warning, (in Projectile) `d` is implicitly declared local

  

Warning, (in Projectile) `eq1` is implicitly declared local

  

Warning, (in Projectile) `eq2` is implicitly declared local

  

Warning, (in Projectile) `j` is implicitly declared local

  

Warning, (in Projectile) `eq11` is implicitly declared local

  
> 

Projectile(1);

int(cos(0.4442882938e-1*z)*cos(1.414213562*z)/e^(z^2), z = -49.49747467 .. 21.21320343)

 (1)
> 

 


Download SolnforProjectile_v3_3.mw

How to verify eq by using (2), (3) and (4)?...

Asked by: WA573 80
differential-equations
May 13 2024
0  2

How to verify eq by using (2), (3) and (4)? Since lambda's, A's, B's and a are constant, but they appear as variables i.e., D[2](A1)..., (D[2] -> d/dt (derivative w.r.t 't')). Also q(n+1,t)- q(n,t) = a (const). Therefore, d/dt(q(n+1),t) - d/dt,(q(n,t))=0

verif_May24.mw

strange window behavior problem...

Asked by: segfault 145
linux
May 12 2024
0  0

OS Linux

I have Maple 2022 open with a worksheet on a specific workspace.

I then move to a different workspace and want to start a new instance of maple for a new problem.

In command line I exacute

$]xmaple22 –standalone  filename.mw

Unfortunately when the new instance is started, the open maple instance on the first workspace is moved automatically to the second workspace together with the new instance opened, completely messing up the organization.

This is not expected behavior.

How can I make Maple execute absolutely independent instances of xmaple22 without indiscressionately and automatically moving existing open maple instances to the current workspace.

Severely annoying. Maple 9.5 e.g. does not have this behavior at all so Maple 2022 is a step backwards in this regard.

Thanks

Implicit functions in Maple...

Asked by: learningmath 10
homework implicitplot tangent
May 09 2024
2  2

Hi everyone,

I'm having trouble in maple to do the following:
Plot the curve x^3-4xy+2y^3=0 , as x variesbetween -3 and 3 with the aid of the implicitplot command

find dy/dx at all points (x,y) on the curve for which x=1. and find the equations of the lines tangent to the curve at the points

plot the curve and tangent lines on the same set of axes

Any help would be appreciated , thank you.

Why does no substitution work on some functions ?...

Asked by: WA573 80
substitution subs
May 06 2024
0  4

Why does no substitution work on functions with s(n+1,t) (see eqns (2-8))? Also (&PartialD;)/(&PartialD; (sigma2*t))=1/(sigma2)(&PartialD;)/(&PartialD; t), how can I do it on Maple?shift.mw

Third party package...

Asked by: mz6687 40
package library
May 06 2024
0  3

I am trying to load the third-party package 'CPC Program Library (qub.ac.uk)' by following the instructions as in 'how to install wkptest? - MaplePrimes'. But encounter with Errors: '

Error, `:` unexpected
with(wkptest);
Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received wkptest

> 

restart:
> 

sourcefolder:=cat(kernelopts('C:\Users\ahmed\Downloads\adty_v1_0'),"/wkptest");
installfolder:=cat(kernelopts('homedir'),"/maple/toolbox/wkptest/lib");
FileTools:-MakeDirectory(installfolder, 'recurse'=true);
libraryfile:=cat(installfolder,"/wkptest.mla");
try
  FileTools:-Remove(libraryfile);
catch:
end try:
LibraryTools:-Create(libraryfile);
libname:=libraryfile,libname;
read cat(sourcefolder,"/wkptest_cpc");

Error, `:` unexpected

  
> 

with(wkptest);

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received wkptest

  
 

 

Download exam_wkptest1.mws

How can I make if-statement work in my code?...

Asked by: Dkunb 70
if-then spelling
May 01 2024
0  1

How can I make if-statement work in my code?
assuming m,n :: integers
Thank you in advance.

> 

restart;
> 

 

> 

x2 := proc(m,n)
  if ((is(m,even) and is(n,odd)) or (is(m,odd)and is(n,even))) then -8*L*m*n/(m+n)^2/Pi^2/(m-n)^2;
  else  0;
  end if;
end poc:

Error, missing operator or `;`

  


Download test2.mw

How do I integrate in Maple?...

Asked by: Dkunb 70
integration
April 30 2024
1  2

How can I  get the result for the integration when m =n or m is not equal to n and How can I add assumption that m, or n can be even or odd?

Thanks in advance for your help.

 
> 

restart;
phi := proc(k,x,L)
  if (type(k,even)) then sqrt(2)*sin(Pi*k*x/L)/sqrt(L)
  else sqrt(2)*cos(Pi*k*x/L)/sqrt(L)
  end if;
end proc:
> 

Int(phi(m,x,L)*_h^2/m2*diff(phi(n,x,L),x,x),x=-L/2..L/2);

Int(-2*cos(Pi*m*x/L)*_h^2*Pi^2*n^2*cos(Pi*n*x/L)/(L^3*m2), x = -(1/2)*L .. (1/2)*L)

 (1)
 

 

Download test1.mw

 

Factor in matrix form...

Asked by: Dkunb 70
matrix factorization simplification
April 16 2024
1  5

ras5_v1.mw 

How can I  change eq13 to eq14 without using op command manually?

Thank you for your help in advance,

HELP WITH A CORRUPTED FILE ASAP!...

Asked by: Bubbleee 5
worksheet corruption
April 15 2024
1  5

Hey! I need help ASAP, because my maple file has been corrupted and i dont know what to do. Do you guys know how to recover a file? i can save it again as_mw. but should i change it to xml? or how? i have the link to my maple file attached, so if someone can help me, it could be helpful! Because i have an upcoming exam. Thanks youu

How can a trigonometric expression, including cos(...

Asked by: Ali Hassani 120
simplification trig
April 09 2024
1  3

 

Dear All,
I want to simplify the following trigonometric expression, considering that m is an integer number. For this, I use the following command:

expr:= 4*cos(Pi*m)/(Pi*(2*m + 1)); 
simplify(%, assume=integer);
factor(%);

However, if I want to simplify the following trigonometric expression, m is an integer number, and alpha is a real number, using the following command will lead to the wrong answer because alpha is also considered an integer number. Please guide me.

4*cos(Pi*m+2*alpha*Pi)/(Pi*(2*m + 1));
simplify(%, assume=integer);
factor(%);

Best wishes

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