In[]:=
ClearAll["Global`*"];
In[]:=
h=
9
10
;m=
9
10
;a=-
9
10
;c1=1;c2=1;
In[]:=
y[b_]:=c1
1
2
+
1+
2
m
2
h
b
+c2
1
2
-
1+
2
m
2
h
b
;
In[]:=
​​y[f_]:=c1
1
2
+
1+
2
m
2
h
f
+c2
1
2
-
1+
2
m
2
h
f
;
In[]:=
eq[k_,q_,b_,f_]=
1
2
h
-
2
k
*Sinh
2
h
-
2
k
(q-b)*
1
(h*b)
2
m
y[b]^2-
1
(h*b)
D[y[b],b]^2+
1
2
h
-
2
k
*Sinh
2
h
-
2
k
(q-f)*
1
(h*b)
2
m
y[f]^2-
1
(h*f)
D[y[f],f]^2;
In[]:=
​​i1[k_?NumericQ,f_?NumericQ,q_?NumericQ]:=i1[k,f,q]=NIntegrate[eq[k,q,b,f],{b,1,q}]
In[]:=
i2[k_?NumericQ,q_?NumericQ]:=i2[k,q]=NIntegrate[i1[k,f,q],{f,1,q},WorkingPrecision30,PrecisionGoal10]
In[]:=
​​i2[5/h,0.001]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 9 recursive bisections in f near {f} = {0.99515386477271439027613986850169920282412314838633669624630535559058055686863013}. NIntegrate obtained -4.1702146290979377895418717902098555889354322548311583825818566748887910661269263×
433860179
10
and 1.0574309208996541670932883132059840025780311059205766510915579917166653763161420×
433860174
10
for the integral and error estimates.
Out[]=
-4.17021462909793778954187179021×
433860179
10