adel-00

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12 years, 8 days

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These are replies submitted by adel-00

@Kitonum @vv 615

Hi,

I split the sysytem above (the real and the imiginary parts) and the system now are three DEs without complex coefficients as:

 

restart:
Dijits:=20:
------------------------- Defining the nature of the variables used ----------------------
assume(t,real):

x(0):=-1:y(0):=1:z(0):=conjugate(y(0)):N:=10:Delta:=5:omega:=10^(6):N1:=1+2*N:M:=sqrt(N*(N+1)):
t0:=0.0:tN:=30.0: M1:=5000;:th:=evalf((tN-t0)/M1):
5000
ini1:=u(0)=Re(y(0)), v(0)=Im(z(0)),w(0)=x(0);
u(0) = 1, v(0) = 0, w(0) = -1
var:={u(t),v(t),w(t)}: 
dsys1 :=diff(w(t),t)=-(N1+M*cos(2*omega*t))*w(t)-1+2*u(t)*cos(2*omega*t)+2*v(t)*sin(2*omega*t), diff(u(t),t)=-N1*u(t)+Delta*v(t)-2*M+(2*M*u(t)-N1-w(t))*cos(2*omega*t)-2*M*v(t)*sin(2*omega*t), diff(v(t),t)=-N1*v(t)-Delta*u(t)+(2*M*u(t)-N1-w(t))*sin(2*omega*t)+2*M*v(t)*cos(2*omega*t):


dsol1 :=dsolve({dsys1,ini1},var,numeric, output=listprocedure, abserr=1e-9, relerr=1e-8,range=0..1,maxfun=5000):


Warning, cannot evaluate the solution further right of .46544244e-3, maxfun limit exceeded (see ?dsolve,maxfun for details)


dsolu:=subs(dsol1,u(t)):dsolv:=subs(dsol1,v(t)):dsolw:=subs(dsol1,w(t)):
t1:=array(0..M1,[]): u1:=array(0..M1,[]): v1:=array(0..M1,[]): w1:=array(0..M1,[]): pt1:=array(0..M1,[]):pt2:=array(0..M1,[]):pt3:=array(0..M1,[]): 
for i from 0 to M1 do t1[i]:=evalf(th*i):u1[i]:=evalf(dsolu(t1[i]));v1[i]:=evalf(dsolv(t1[i])):w1[i]:=evalf(dsolw(t1[i])):pt1[i]:=[t1[i],u1[i]]:pt2[i]:=[t1[i],v1[i]]:pt3[i]:=[t1[i],w1[i]]:od:


Error, (in dsolu) cannot evaluate the solution further right of 0.46544244e-3, maxfun limit exceeded (see ?dsolve,maxfun for details)


with(plots):
unassign('i'):mytab1:=[seq(pt1[i],i=0..M1)]:mytab2:=[seq(pt2[i],i=0..M1)]:mytab3:=[seq(pt3[i],i=0..M1)]:
plot(mytab3,t=0..5,tickmarks=[6, 6],axes=boxed);

I got the underlines error. PLZ Mr. Kitonum and W 615 looking forward for your advise. Many thanks.

when I set the maxfun=10^9

the message apeares:

Warning, extending a solution obtained using the range argument with 'maxfun' large or disabled is highly inefficient, and may consume a great deal of memory. If this functionality is desired, it is suggested to call dsolve without the range argument
Warning, computation interrupted

Please and comments or addvise will be helpful

Warning, cannot evaluate the solution further right of .31089494e-2, maxfun limit exceeded (see ?dsolve,maxfun for details)

This is the message!

I got this ouput:

Warning, cannot evaluate the solution further right of .26120132e-2, maxfun limit exceeded (see ?dsolve,maxfun for details)

I seperate the variables in Real and Imigneray parts,  as follows:

restart:
Dijits:=20:
------------------------- Defining the nature of the variables used ----------------------
assume(t,real):

x(0):=-1:y(0):=1:z(0):=conjugate(y(0)):N:=10:Delta:=5:omega:=10^(6):N1:=1+2*N:M:=sqrt(N*(N+1)):
t0:=0.0:tN:=30.0: M1:=5000;:th:=evalf((tN-t0)/M1):
5000
ini1:=u(0)=Re(y(0)), v(0)=Im(z(0)),w(0)=x(0);
u(0) = 1, v(0) = 0, w(0) = -1
var:={u(t),v(t),w(t)}: 
dsys1 :=diff(w(t),t)=-(N1+M*cos(2*omega*t))*w(t)-1+2*u(t)*cos(2*omega*t)+2*v(t)*sin(2*omega*t), diff(u(t),t)=-N1*u(t)+Delta*v(t)-2*M+(2*M*u(t)-N1-w(t))*cos(2*omega*t)-2*M*v(t)*sin(2*omega*t), diff(v(t),t)=-N1*v(t)-Delta*u(t)-2*M+(2*M*u(t)-N1-w(t))*sin(2*omega*t)+2*M*v(t)*cos(2*omega*t):
dsol1 :=dsolve({dsys1,ini1},var,numeric, output=listprocedure, abserr=1e-9, relerr=1e-8,range=0..1,maxfun=5000):
Warning, cannot evaluate the solution further right of .46544244e-3, maxfun limit exceeded (see ?dsolve,maxfun for details)
dsolu:=subs(dsol1,u(t)):dsolv:=subs(dsol1,v(t)):dsolw:=subs(dsol1,w(t)):
t1:=array(0..M1,[]): u1:=array(0..M1,[]): v1:=array(0..M1,[]): w1:=array(0..M1,[]): pt1:=array(0..M1,[]):pt2:=array(0..M1,[]):pt3:=array(0..M1,[]): 
for i from 0 to M1 do t1[i]:=evalf(th*i):u1[i]:=evalf(dsolu(t1[i]));v1[i]:=evalf(dsolv(t1[i])):w1[i]:=evalf(dsolw(t1[i])):pt1[i]:=[t1[i],u1[i]]:pt2[i]:=[t1[i],v1[i]]:pt3[i]:=[t1[i],w1[i]]:od:
Error, (in dsolu) cannot evaluate the solution further right of 0.46544244e-3, maxfun limit exceeded (see ?dsolve,maxfun for details)


with(plots):
unassign('i'):mytab1:=[seq(pt1[i],i=0..M1)]:mytab2:=[seq(pt2[i],i=0..M1)]:mytab3:=[seq(pt3[i],i=0..M1)]:
plot(mytab3,t=0..5,tickmarks=[6, 6],axes=boxed);

@adel-00 

I seperate the DE sys to real and imegenary parts but idont no why it takes long time to excute this the prog. below:

restart;
Digits:=40:
epsilon:=0.01:Delta1:=20:Delta2:=20: N1:=1000:
dsys :={diff(x1(t),t)=-Delta2*x2(t)+y1(t)*epsilon, diff(x2(t),t)=Delta1*x1(t)+y2(t)*epsilon,diff(y1(t),t)=Delta2*y2(t)+x1(t)*z(t), diff(y2(t),t)=z(t)*x2(t)-y1(t)*Delta2, diff(z(t),t)=-4*x2(t)*y2(t)-4*y1(t)*x1(t)}:

res:=dsolve(dsys union {x1(0)=0,x2(0)=0.2,y1(0)=0,y2(0)=0,z(0)=-1},numeric,output=listprocedure,maxfun=0):

 

plots[odeplot](res,[[t,y2(t)]],0..2000,axes=boxed,titlefont=[SYMBOL,14],font=[1,1,18],color=black,linestyle=1,tickmarks=[3, 4],font=[1,1,14],thickness=2,titlefont=[SYMBOL,12],view=[0..2000,-0.5..0.5]);

I appreciate any comments

Regards

@Preben Alsholm 

In general these are the steady state of the sys:

where Delta1 , Delta2,c, epsilon are arbtrary

X=∆1/∆1∆2+c

Y= -εc / ∆1∆1 +c

Z=

Thanks for yorr fast reply

@Preben Alsholm 

 

the steady state value i do it analyticaly which is constant value so any plots of the solutions is oscillate for large tme never stop>>

 

it should give the steady state for large t but i can not get it for all solutions is that because the sys is complex ?? so im thinking to seperate the sys in Re and Im to be 5 equations (Note x(t), y(t) are complex and z(t) is real)

Thanks

@adel-00 

dsolve(dsys union {x(0)=0,y(0)=0,z(0)=-1},numeric,output=listprocedure,maxfun=0);

but it oscillates doesnt give me steady state!!!

@Markiyan Hirnyk 

Yes it should be oscilate to reach the steady state

 

still give this msg.

Warning, cannot evaluate the solution further right of 108.54989, maxfun limit exceeded (see ?dsolve,maxfun for details)
Error, (in plot/options2d) unexpected option: maxfun = 0

 

Do I need to seperate the DEs inreal and imeginary parts?

I got confused with Latex

Thanks

@Preben Alsholm 

also from the plots are clear many thanks

last quaestion please how to get the steady state value

@Preben Alsholm 

Thanks ..are there any ways to get the actual number of the excepression 0.25*z(t)^2+Re(y(t))^2+Im(y(t)) 

the results should be 0.06

 

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