How to solve coupled linear differential equations ?
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I am trying to solve 9 linear coupled differential equations using "dsolve". In the out put error is showing up which i couldn't understood, and Matlab is shutting down once i run the program. What i expect in the out put is 9 equations as function of time only. My 9 variables are p11, p12, p21, p22, p23, p33, p32, p31, p13. I want to see the out put of this differential equations p11'(t)=..., p12'(t)=...etc, as p11(t)=F[t], p12(t)=F[t].. etc. Here are the equations which i am trying to solve.
syms p11(t) p12(t) p21(t) p22(t) p13(t) p32(t) p23(t) p33(t) p31(t)
[p11, p12, p21, p22, p13, p31, p33, p23, p32] = dsolve((diff(p11)==vpa((0.5E-3+(-0.1E-2)).*p11+(sqrt(-1)*(-1)).*vpa((0.5E0).* ...
p13+(-1/2).*p31)+vpa(0.5E-2.*p33))),(diff(p12)==(vpa((-0.1E-2)).*p12+( ...
sqrt(-1)*(-1)).*vpa((0.2E0).*p12+vpa(0.55E0).*p13+(-1/2).*p32))),(diff( ...
p13)==(vpa((-0.6E-2)).*p13+(sqrt(-1)*(-1)).*((1/2).*p11+vpa(0.55E0).*p12+vpa(0.1E0).* ...
p13+(-1/2).*p33))), (diff(p21)==(vpa(-0.1E-2).*p21+(sqrt(-1)*(-1)) ...
.*(vpa(-0.2E0).*p21+0.5E0.*p23+vpa(-0.55E0).*p31))),(diff(p22)==(vpa( ...
0.5E-3)+vpa(-0.1E-2).*p22+(sqrt(-1)*(-1)).*(vpa(0.55E0).*p23+vpa(-0.55E0).*p32)+ ...
vpa(0.5E-2).*p33)),(diff(p23)==(vpa(-0.6E-2).*p23+(sqrt(-1)*(-1)).*(( ...
1/2).*p21+vpa(0.55E0).*p22+vpa(-0.1E0).*p23+vpa(-0.55E0).*p33))),((diff(p31) ...
==(vpa(-0.6E-2).*p31+(sqrt(-1)*(-1)).*(vpa(-0.5E0).*p11+vpa(-0.55E0).*p21+( ...
-0.1E0).*p31+0.5E0.*p33)))),(diff(p32)==(vpa(-0.6E-2).*p32+(sqrt( ...
-1)*(-1)).*(vpa(-0.5E0).*p12+vpa(-0.55E0).*p22+0.1E0.*p32+0.55E0.*p33))),( ...
diff(p33)==((sqrt(-1)*(-1)).*(vpa(-0.5E0).*p13+(-0.55E0).*p23+( ...
1/2).*p31+vpa(0.55E0).*p32)+vpa(-0.11E-1).*p33)),p11(0)==(1),p12(0)==(0),p13(0)==(0),p21(0)==(0),p22(0)==(0), ...
p23(0)==(0),p31(0)==(0),p32(0)==(0),p33(0)==(0), t)
Can any one help me please ?
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