## 135 Reputation

12 years, 125 days

## new sys...

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.

## maxfun=10^9...

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

## Error...

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

This is the message!

## error...

I got this ouput:

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

## IVP...

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);

## long time...

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]);

Regards

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=

## @Preben Alsholm    the steady ...

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

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 ...

Yes it should be oscilate to reach the steady state

## Error...

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?

## many thanks...

I got confused with Latex

Thanks

also from the plots are clear many thanks

## actual number of the excepression...

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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