# Question:How do I solve complx Ivp

## Question:How do I solve complx Ivp

Maple 13

 > restart:pt:=1000:Digits:=65:
 > epsilon:=0:Delta1:=1:Delta2:=5:Delta2:=1:x(0):=0.0:y(0):=0:z(0):=-1:t0:=0:tN:=5: N1:=5000;th:=evalf((tN-t0)/N1):
 (1)
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 > #tit:=sprintf("W=%g,D=%g,f=%g,d=%g,k=%d,N=%g",Omega,Delta,phi,delta,k,N);
 > sys1:={diff(x(t),t)=I*Delta1*x(t)+y(t)+epsilon,diff(y(t),t)=-I*Delta2*y(t)+x(t)*z(t),diff(z(t),t)=-2*(conjugate(x(t))*y(t)+x(t)*conjugate(y(t)))};
 (2)
 > incs:=xr(0),xI(0),yr(0),yi(0)=0,zr(0)=-1,zi(0)=0:
 > bigsys := sys1:
 > functions := indets(bigsys, anyfunc(identical(t))):
 > redefinitions := map(f -> f = cat(op(0, f), _R)(t) + I*cat(op(0,f), _I)(t), functions):
 > #newfunctions := indets(redefinitions, anyfunc(identical(t))) minus functions;
 > bigsys_separated := eval(bigsys, redefinitions):
 > newsys := map(evalc @ Re, bigsys_separated) union map(evalc @ Im, bigsys_separated):
 > incs := {x_R(0)=0, x_I(0)=0, y_R(0)=0, y_I(0)=0,z_R(0)=-1, z_I(0)=0,x_R(0)=0, x_I(0)=0, y_R(0)=0, y_I(0)=0, z_R(0)=-1, z_I(0)=0}:
 >
 (3)
 > solution := dsolve(newsys union incs, numeric,bigsys);
 > with(plots):
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 > plots[odeplot](solution, [t, x_R(t)], 0..5,axes=boxed,thickness=2,numpoints=pt,color=black,legend=[z(t)]);
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