create a list which will get updated,after a run

Questions
1

(wish to store outputs of e0, e1, e2 in list ee0, ee1,ee2 respectively)
v1=10.;

v2=10.;
v3=10.;

a=5.;

b1=0.1;

b2=-b1;

c=5.;

p[e_]:=Sqrt[v1-e];

k[e_]:=Sqrt[e];

r[e_]:=Sqrt[e-v2];

q[e_]:=Sqrt[v3-e];

a2[e_]:=(p[e]*Cos[k[e]*a]-k[e]*Sin[k[e]*a]);

a22[e_]:=(k[e]*Cos[k[e]*a]+p[e]*Sin[k[e]*a]);

a1[e_]:=(k[e]*Sin[k[e]*c]-q[e]*Cos[k[e]*c]);

a11[e_]:=(q[e]*Sin[k[e]*c]+k[e]*Cos[k[e]*c]);

c1[e_]:=a11[e]*k[e]*Sin[k[e]*b2]*Cos[r[e]*b2]-a11[e]*r[e]*Cos[k[e]*b2]*Sin[r[e]b2]+a1[e](k[e]*Cos[r[e]*b2]*Cos[k[e]*b2]+r[e]*Sin[k[e]*b2]*Sin[r[e]*b2]);

c2[e_]:=a1[e]*(k[e]*Sin[r[e]*b2]*Cos[k[e]*b2]-r[e]*Sin[k[e]*b2]*Cos[r[e]*b2])-a11[e]*k[e]*Sin[r[e]*b2]*Sin[k[e]*b2]-a11[e]*r[e]*Cos[r[e]*b2]*Cos[k[e]*b2];

c3[e_]:=a22[e]*r[e]*Cos[k[e]*b1]*Sin[r[e]*b1]-a22[e]*k[e]*Cos[r[e]*b1]*Sin[k[e]b1]+a2[e](r[e]*Sin[k[e]*b1]*Sin[r[e]*b1]+k[e]*Cos[r[e]*b1]*Cos[k[e]*b1]);

c4[e_]:=a2[e]*(r[e]*Sin[k[e]*b1]*Cos[r[e]*b1]-k[e]*Sin[r[e]*b1]*Cos[k[e]*b1])+a22[e]*r[e]*Cos[r[e]*b1]*Cos[k[e]*b1]+a22[e]*k[e]*Sin[r[e]*b1]*Sin[k[e]*b1];

f[e_]:=c1[e]*c4[e]-c3[e]*c2[e];

Plot[{Im[f[e]],Re[f[e]]},{e,0.348,0.350}]

FindRoot[f[e]==0,{e,30}]

e0=Join[{b2,Re[e/.%]}]

FindRoot[f[e]==0,{e,0.3}];

e1=Join[{b2,Re[e/.%]}]

FindRoot[f[e]==0,{e,0.4}];

e2=Join[{b2,Re[e/.%]}]

ee0={{1,0.0910614}};

ee1={{1,0.358352}};

ee2={{1,0.394396}};
(wish to store outputs of e0, e1, e2 in list ee0, ee1,ee2 respectively)

2

Is there anything preventing using,

AppendTo[ee0, e0];(*And similarly for the other results.*)
3

(wish to store outputs of e0, e1, e2 in list ee0, ee1,ee2 respectively)
v1=10.;

v2=10.;
v3=10.;

a=5.;

b1=0.1;

b2=-b1;

c=5.;

p[e_]:=Sqrt[v1-e];

k[e_]:=Sqrt[e];

r[e_]:=Sqrt[e-v2];

q[e_]:=Sqrt[v3-e];

a2[e_]:=(p[e]*Cos[k[e]*a]-k[e]*Sin[k[e]*a]);

a22[e_]:=(k[e]*Cos[k[e]*a]+p[e]*Sin[k[e]*a]);

a1[e_]:=(k[e]*Sin[k[e]*c]-q[e]*Cos[k[e]*c]);

a11[e_]:=(q[e]*Sin[k[e]*c]+k[e]*Cos[k[e]*c]);

c1[e_]:=a11[e]*k[e]*Sin[k[e]*b2]*Cos[r[e]*b2]-a11[e]*r[e]*Cos[k[e]*b2]*Sin[r[e]b2]+a1[e](k[e]*Cos[r[e]*b2]*Cos[k[e]*b2]+r[e]*Sin[k[e]*b2]*Sin[r[e]*b2]);

c2[e_]:=a1[e]*(k[e]*Sin[r[e]*b2]*Cos[k[e]*b2]-r[e]*Sin[k[e]*b2]*Cos[r[e]*b2])-a11[e]*k[e]*Sin[r[e]*b2]*Sin[k[e]*b2]-a11[e]*r[e]*Cos[r[e]*b2]*Cos[k[e]*b2];

c3[e_]:=a22[e]*r[e]*Cos[k[e]*b1]*Sin[r[e]*b1]-a22[e]*k[e]*Cos[r[e]*b1]*Sin[k[e]b1]+a2[e](r[e]*Sin[k[e]*b1]*Sin[r[e]*b1]+k[e]*Cos[r[e]*b1]*Cos[k[e]*b1]);

c4[e_]:=a2[e]*(r[e]*Sin[k[e]*b1]*Cos[r[e]*b1]-k[e]*Sin[r[e]*b1]*Cos[k[e]*b1])+a22[e]*r[e]*Cos[r[e]*b1]*Cos[k[e]*b1]+a22[e]*k[e]*Sin[r[e]*b1]*Sin[k[e]*b1];

f[e_]:=c1[e]*c4[e]-c3[e]*c2[e];

Plot[{Im[f[e]],Re[f[e]]},{e,0.348,0.350}]

FindRoot[f[e]==0,{e,30}]

e0=Join[{b2,Re[e/.%]}]

FindRoot[f[e]==0,{e,0.3}];

e1=Join[{b2,Re[e/.%]}]

FindRoot[f[e]==0,{e,0.4}];

e2=Join[{b2,Re[e/.%]}]

ee0={{1,0.0910614}};

ee1={{1,0.358352}};

ee2={{1,0.394396}};
(wish to store outputs of e0, e1, e2 in list ee0, ee1,ee2 respectively)

4

Thanks man … You are awesome Isaac … My issue is solved now … My workload is reduced to 1/20 and now I can find out 500 eigenvalues in just 5 mins … which previously took me more than a day …
I just need to do a small trick of commenting the list ee0 and run the code 500 times then I copy the complete output to the ee0 list in the code …
Thanks again man …