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Ali Guzel

Mr. Ali Guzel

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19 years, 111 days
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Maple 9.5 example, in later version...

Ali Guzel 80 Maple
sum dsolve series
May 30 2026
0 5

05-2-2.mws

Can you help me with this code?

> 

restart: with(VectorCalculus):

> 

assume(g>0,Omega>0,V0>0,theta>0,alpha>0,alpha<=Pi/2):
> 

alias(omega=w,Omega=W,alpha=a):
> 

w:=<-W*cos(a),0,W*sin(a)>;

Vector(3, {(1) = -W*cos(a), (2) = 0, (3) = W*sin(a)})

 (1)
> 

r:=<x(t),y(t),z(t)>; v:=diff(r,t);

Vector(3, {(1) = x(t), (2) = y(t), (3) = z(t)})

Vector(3, {(1) = diff(x(t), t), (2) = diff(y(t), t), (3) = diff(z(t), t)})

 (2)
> 

F[gravity]:=<0,0,-g>;

Vector(3, {(1) = 0, (2) = 0, (3) = -g})

 (3)
> 

F[Coriolis]:=-2*w &x v;

Vector(3, {(1) = 2*W*sin(a)*(diff(y(t), t)), (2) = -2*W*cos(a)*(diff(z(t), t))-2*W*sin(a)*(diff(x(t), t)), (3) = 2*W*cos(a)*(diff(y(t), t))})

 (4)
> 

F[centrifugal]:=-w &x (w &x r);

Vector(3, {(1) = W*sin(a)*(W*cos(a)*z(t)+W*sin(a)*x(t)), (2) = W^2*cos(a)^2*y(t)+W^2*sin(a)^2*y(t), (3) = W*cos(a)*(W*cos(a)*z(t)+W*sin(a)*x(t))})

 (5)
> 

F[resultant]:=F[gravity]+F[Coriolis]+F[centrifugal];

Vector(3, {(1) = 2*W*sin(a)*(diff(y(t), t))+W*sin(a)*(W*cos(a)*z(t)+W*sin(a)*x(t)), (2) = -2*W*cos(a)*(diff(z(t), t))-2*W*sin(a)*(diff(x(t), t))+W^2*cos(a)^2*y(t)+W^2*sin(a)^2*y(t), (3) = -g+2*W*cos(a)*(diff(y(t), t))+W*cos(a)*(W*cos(a)*z(t)+W*sin(a)*x(t))})

 (6)
> 

eq:=(u,i)->simplify(diff(u(t),t,t)=F[resultant][i]):
> 

xeq:=eq(x,1); yeq:=eq(y,2); zeq:=eq(z,3);

xeq := diff(x(t), `$`(t, 2)) = Omega*sin(alpha)*(Omega*sin(alpha)*x(t)+Omega*cos(alpha)*z(t)+2*(diff(y(t), t)))

yeq := diff(y(t), `$`(t, 2)) = Omega*(y(t)*Omega-2*(diff(z(t), t))*cos(alpha)-2*(diff(x(t), t))*sin(alpha))

zeq := diff(z(t), `$`(t, 2)) = sin(alpha)*cos(alpha)*x(t)*Omega^2+cos(alpha)^2*z(t)*Omega^2+2*Omega*cos(alpha)*(diff(y(t), t))-g

 (7)
> 

ic:=x(0)=0,y(0)=0,z(0)=0,D(x)(0)=0,D(y)(0)=V0*cos(theta),D(z)(0)=V0*sin(theta);

ic := x(0) = 0, y(0) = 0, z(0) = 0, (D(x))(0) = 0, (D(y))(0) = V0*cos(theta), (D(z))(0) = V0*sin(theta)

 (8)
> 

sol:=dsolve({xeq,yeq,zeq,ic},{x(t),y(t),z(t)},method=laplace):

> 

assign(sol):
> 

f:=u->simplify(expand(u(t))): X:=f(x); Y:=f(y); Z:=f(z);

X := -(1/4)*(Omega^4*V0*sin(theta)*cos(alpha)*(sum(exp(_alpha1*t)/((Omega^2+_alpha1^2)*_alpha1), _alpha1 = RootOf(Omega^2+_Z^2)))+cos(alpha)*g*(sum(exp(_alpha1*t)*_alpha1^2/(Omega^2+_alpha1^2), _alpha1 = RootOf(Omega^2+_Z^2)))-sin(theta)*cos(alpha)*V0*(sum(exp(_alpha1*t)*_alpha1/(Omega^2+_alpha1^2), _alpha1 = RootOf(Omega^2+_Z^2)))*Omega^2+(-2*Omega^3*cos(theta)*V0+3*cos(alpha)*Omega^2*g)*(sum(exp(_alpha1*t)/(Omega^2+_alpha1^2), _alpha1 = RootOf(Omega^2+_Z^2)))+4*(Omega^2*t*V0*sin(theta)-(1/2)*Omega^2*t^2*g-g)*cos(alpha))*sin(alpha)/Omega^2

Y := (1/4)*(-V0*cos(theta)*Omega^2+2*cos(alpha)*Omega*g)*(sum(exp(_alpha1*t)/((Omega^2+_alpha1^2)*_alpha1), _alpha1 = RootOf(Omega^2+_Z^2)))-(1/2)*sin(theta)*cos(alpha)*V0*Omega*(sum(exp(_alpha1*t)/(Omega^2+_alpha1^2), _alpha1 = RootOf(Omega^2+_Z^2)))+(1/4)*V0*cos(theta)*(sum(exp(_alpha1*t)*_alpha1/(Omega^2+_alpha1^2), _alpha1 = RootOf(Omega^2+_Z^2)))

Z := (1/4)*(-Omega^4*cos(alpha)^2*V0*sin(theta)*(sum(exp(_alpha1*t)/((Omega^2+_alpha1^2)*_alpha1), _alpha1 = RootOf(Omega^2+_Z^2)))-cos(alpha)^2*g*(sum(exp(_alpha1*t)*_alpha1^2/(Omega^2+_alpha1^2), _alpha1 = RootOf(Omega^2+_Z^2)))+cos(alpha)^2*sin(theta)*V0*(sum(exp(_alpha1*t)*_alpha1/(Omega^2+_alpha1^2), _alpha1 = RootOf(Omega^2+_Z^2)))*Omega^2+(2*Omega^3*cos(alpha)*cos(theta)*V0-3*Omega^2*g*cos(alpha)^2)*(sum(exp(_alpha1*t)/(Omega^2+_alpha1^2), _alpha1 = RootOf(Omega^2+_Z^2)))+(-4*Omega^2*t*V0*sin(theta)+2*Omega^2*t^2*g+4*g)*cos(alpha)^2+4*Omega^2*t*V0*sin(theta)-2*Omega^2*t^2*g)/Omega^2

 (9)
> 

P:=(u,n)->convert(taylor(u,W=0,n),polynom):

> 

Xexp:=P(X,4); Yexp:=P(Y,4); Zexp:=P(Z,4);  

Error, (in series/sum) unable to compute series

Error, (in series/sum) unable to compute series

Error, (in series/sum) unable to compute series

  
> 

tt:=solve(Zexp=0,t);

tt :=

(10)
> 

 T1:=P(tt[2],1); d[x]:=eval(Xexp,t=T1);  

Error, invalid subscript selector

d[x] := Xexp

  
> 

T2:=P(tt[2],2); d[y]:=P(eval(Yexp,t=T2),2);

Error, invalid subscript selector

d[y] := Yexp

  
> 

d[y]:=collect(d[y],[cos(a),1/g^2,V0^3,W]);

d[y] := Yexp

 (11)
> 

parameters:={a=Pi/4,theta=Pi/3,V0=500,W=7.27*10^(-5),g=9.8}:

> 

d[x]:=eval(d[x],evalf(parameters));

d[x] := Xexp

 (12)
> 

d[y]:=eval(d[y],evalf(parameters));

d[y] := Yexp

 (13)
 

 

Download 05-2-2.mws

Cannot plot numerical ode...

Ali Guzel 80 Maple 6
ode dsolve numeric
May 29 2026
2 2

Can anyone help me?

> 

restart: with(plots):   
> 

h:=0.01: n:=6000: Digits:=18:
> 

t[0]:=0: x[0]:=0.2: y[0]:=0.1: epsilon:=20:

> 

F:=(x,y)->epsilon*(1-x^2)*y-x:
> 

begin:=time():
> 

for k from 0 to n do
> 

t[k+1]:=t[k]+h;
> 

x[k+1]:=x[k]+h*y[k];
> 

y[k+1]:=y[k]+h*F(x[k],y[k]);
> 

pt[k]:=[t[k],x[k],y[k]]:

> 

end do:
> 

cpu_time:=time()-begin;
> 

pointplot3d([seq(pt[j],j=0..n)],axes=normal,symbol=cross,symbolsize=8,color=red,labels=["t","x","y"],orientation=[-90,0]);
> 

sys:=diff(X(t),t)=Y(t),diff(Y(t),t)=F(X(t),Y(t));
> 

vars:={X(t),Y(t)}: ic:=X(0)=0.2,Y(0)=0.1:
> 

sol:=dsolve({sys,ic},vars,numeric,stepsize=h,method=classical[foreuler],output=listprocedure):
> 

odeplot(sol,[t,X(t)],0..h*n,axes=normal,style=line,numpoints=n,labels=["t","x"]);
> 

XX:=eval(X(t),sol): x1:=XX(1);  pt[100];
 

 

Download 09-1-1.mws

Is it possible?...

Ali Guzel 80 Maple
ode spacecurve dsolve
February 01 2025
0 19

Hi All,

Maple is changing fast. It is not possible to run some older codes. 

Is it possible those who have a valid Maple license to have the old versions free of charge?

I have Maple 7, 2018, 2021 licenses but still have problem running older codes.

DirectSearch finds nonexisting roots...

Ali Guzel 80 Maple 2018
rootfinding directsearch
May 03 2022
3 7

DirectSearch finds nonexisting roots....     DirectSearch_finds_nonexisting_roots.mw

> 

 

> 

restart
> 

plot([cos(x), 0.001*x*x],x=-40..40,y=0..2)     ### test function plot

 
> 

eq:= cos(x)= 0.001*x*x;     ###   float

cos(x) = 0.1e-2*x^2

 (1)
> 

use RealDomain in solve(eq,x,explicit) end use   ## lacking some of the roots

-7.793210110, 7.793210110, -11.11953559, 11.11953559, -4.734809278, 4.734809278, -1.568336644, 1.568336644

 (2)
> 

use RealDomain in solve(eq,x) end use

-7.793210110, 7.793210110, -11.11953559, 11.11953559, -4.734809278, 4.734809278, -1.568336644, 1.568336644

 (3)
> 

fsolve(eq,x=-30)

-31.17938383

 (4)
> 

plot([cos(x), 0.001*x*x],x=-32..-31,y=0.9..1)

 
> 

fsolve(eq,x=-32..-30);  fsolve(eq,x=-31.7..-31.4)

-31.17938383

  

-31.52634294

 (5)
> 

with(DirectSearch)

[BoundedObjective, CompromiseProgramming, DataFit, ExponentialWeightedSum, GlobalOptima, GlobalSearch, Minimax, ModifiedTchebycheff, Search, SolveEquations, WeightedProduct, WeightedSum]

 (6)
> 

eq;
SolveEquations(eq,AllSolutions):

cos(x) = 0.1e-2*x^2

 (7)
> 

interface(rtablesize=90);
SolveEquations(eq, AllSolutions)

90

  

Matrix(%id = 4800942722)

 (8)

DirectSearch finds nonexisting roots!!!

Dr. Ali GÜZEL

> 

 

Download DirectSearch_finds_nonexisting_roots.mw

What am I missing in using numboccur?...

Ali Guzel 80 Maple 2018
statistics numoccur
November 07 2021
4 7

restart; p := .5; n := 10; nseq := 2; with(Statistics); randomize(); x1 := seq(Sample(RandomVariable(BernoulliDistribution(p)), n), i = 1 .. nseq); x2 := seq(convert(x1[i], list), i = 1 .. nseq)

[HFloat(0.0), HFloat(1.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(1.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(1.0)], [HFloat(0.0), HFloat(1.0), HFloat(1.0), HFloat(1.0), HFloat(0.0), HFloat(0.0), HFloat(1.0), HFloat(0.0), HFloat(0.0), HFloat(0.0)]

 (1)

x2[1]

[HFloat(0.0), HFloat(1.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(1.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(1.0)]

 (2)

whattype(x2[1])

list

 (3)

numboccur(x2[1], {0.})

0

 (4)

NULL

But, when I plugged the list at (2) it works...  

numboccur([0., 0., 1., 1., 0., 0., 1., 0., 0., 0.], 0.)

7

 (5)

``

NULL

NULL

Download numboccur.mwnumboccur.mw

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