Test of D[ParametricFunction_,_] inside ParallelDo

In[]:=
Λs={2,5,10};(*listofvaluesforParallelDocycle*)​​Km=8;k=∞;μ=1;ν=2;(*particularparametersfromouterDocyclenotshownhere*)​​​​"Boundary condition at z=1: BC1[β_,K_,Λ_]"(*usedinRootSearch*);​​BC1[β_,K_,Λ_]=-
(-1+K)(3
2
K
-2β)βϕ[1]
2(
2
K
-β)(
2
K
-β+
2
K
Λ)
;​​BC1b[β_,K_,Λ_]=D[BC1[β,K,Λ],β];​​​​"Equation to be solved: eqn=";​​eqn=49β1-
64
2
(8-7z)
β(128-
2
(8-7z)
β)
2
(512-8
2
(8-7z)
β)
ϕ[z]+
1
2
(512-8
2
(8-7z)
β)
6272β(32(-1+z)
3
z
2
β
-
4
z
2
β
+64
2
z
β(1-6
2
(-1+z)
β)+1024(-1+z)zβ(-1+2
2
(-1+z)
β)+4096(-2+
2
(-1+z)
β-
4
(-1+z)
2
β
))ϕ[z]+56(8-7z)β
′
ϕ
[z]+4(64-
2
(8-7z)
β+64Λ)
′′
ϕ
[z]0,ϕ[0]1,
′
ϕ
[0]
7β(-3+2β)ϕ[0]
16(-1+β)(-1+β-Λ)
;​​​​"Solution of ParametricNDSolve:";​​sol1p=ParametricNDSolve[eqn,ϕ,{z,0,1},{{β,0,1},{Λ,1,1000}}];​​ϕ1p[z_,β_,Λ_]=ϕ[β,Λ][z]/.sol1p;​​Print["ϕ1p[z,β,Λ]=",ϕ1p[z,β,Λ]];​​ϕ1p1z[z_,β_,Λ_]=D[ϕ1p[z,β,Λ],z]​​ϕ1p1b[z_,β_,Λ_]=D[ϕ1p[z,β,Λ],β]​​(*=====================================================================*)​​DistributeDefinitions[ϕ1p,ϕ1p1z,ϕ1p1b,BC1];​​βm=0.4;​​"Do cycle ===================== "​​Do[​​LHS[β_]=ϕ1p[1,β,Λm];​​Print["LHS[β]=",LHS[β],"\nϕ1p[1,β,Λm]=",ϕ1p[1,β,Λm]];​​​​LHS1b[β_]=D[ϕ1p[1,β,Λm],β];​​Print["LHS1b[β]=",Short[LHS1b[β],3],"\nϕ1p1b[1,β,Λm]=",ϕ1p1b[1,β,Λm]];​​Print["LHS1b[βm]=",Short[LHS1b[βm],3],"\nϕ1p1b[1,βm,Λm]=",ϕ1p1b[1,βm,Λm]];​​​​LHS1z[z_,β_]=D[ϕ1p[z,β,Λm],z];​​Print["LHS1z[β]=",Short[LHS1z[z,β],3],"\nϕ1p1z[z,β,Λm]=",ϕ1p1z[z,β,Λm]];​​Print["LHS1z[0.5,βm]=",Short[LHS1z[0.5,βm],3],"\nϕ1p1z[0.5,βm,Λm]=",ϕ1p1z[0.5,βm,Λm]];​​​​RHS[β_]=BC1[β,Km,Λm];​​Print["D[RHS[β],β]=",D[RHS[β],β],"\nBC1b[β,Km,Λm]=",BC1b[β,Km,Λm]];​​,{Λm,Λs}​​];​​​​"ParallelDo cycle ============= "​​ParallelDo[​​LHS[β_]=ϕ1p[1,β,Λm];​​Print["LHS[β]=",LHS[β],"\nϕ1p[1,β,Λm]=",ϕ1p[1,β,Λm]];​​​​LHS1b[β_]=D[ϕ1p[1,β,Λm],β];​​Print["LHS1b[β]=",Short[LHS1b[β],3],"\nϕ1p1b[1,β,Λm]=",ϕ1p1b[1,β,Λm]];​​Print["LHS1b[βm]=",Short[LHS1b[βm],3],"\nϕ1p1b[1,βm,Λm]=",ϕ1p1b[1,βm,Λm]];​​​​LHS1z[z_,β_]=D[ϕ1p[z,β,Λm],z];​​Print["LHS1z[β]=",Short[LHS1z[z,β],3],"\nϕ1p1z[z,β,Λm]=",ϕ1p1z[z,β,Λm]];​​Print["LHS1z[0.5,βm]=",Short[LHS1z[0.5,βm],3],"\nϕ1p1z[0.5,βm,Λm]=",ϕ1p1z[0.5,βm,Λm]];​​​​RHS[β_]=BC1[β,Km,Λm];​​Print["D[RHS[β],β]=",D[RHS[β],β],"\nBC1b[β,Km,Λm]=",BC1b[β,Km,Λm]];​​,{Λm,Λs}​​];​​
ϕ1p[z,β,Λ]=ParametricFunction
Expression: ϕ
Parameters: {β,Λ}
[β,Λ][z]
Out[]=
′
ParametricFunction
Expression: ϕ
Parameters: {β,Λ}
[β,Λ]
[z]
Out[]=
ParametricFunction
Expression:
∂
β
ϕ
Parameters: {β,Λ}
[β,Λ][z]
Out[]=
Do cycle =====================
LHS[β]=ParametricFunction
Expression: ϕ
Parameters: {β,Λ}
[β,2][1]ϕ1p[1,β,Λm]=ParametricFunction
Expression: ϕ
Parameters: {β,Λ}
[β,2][1]
LHS1b[β]=ParametricFunction
Expression:
∂
β
ϕ
Parameters: {β,Λ}
[β,2][1]ϕ1p1b[1,β,Λm]=ParametricFunction
Expression:
∂
β
ϕ
Parameters: {β,Λ}
[β,2][1]
LHS1b[βm]=-0.412099ϕ1p1b[1,βm,Λm]=-0.412099
LHS1z[β]=
′
ParametricFunction
Expression: ϕ
Parameters: {β,Λ}
[β,2]
[z]ϕ1p1z[z,β,Λm]=
′
ParametricFunction
Expression: ϕ
Parameters: {β,Λ}
[β,2]
[z]
LHS1z[0.5,βm]=-0.140219ϕ1p1z[0.5,βm,Λm]=-0.140219
D[RHS[β],β]=-
7(192-2β)ϕ[1]
2(64-β)(192-β)
-
7(192-2β)βϕ[1]
2(64-β)
2
(192-β)
-
7(192-2β)βϕ[1]
2
2
(64-β)
(192-β)
+
7βϕ[1]
(64-β)(192-β)
BC1b[β,Km,Λm]=-
7(192-2β)ϕ[1]
2(64-β)(192-β)
-
7(192-2β)βϕ[1]
2(64-β)
2
(192-β)
-
7(192-2β)βϕ[1]
2
2
(64-β)
(192-β)
+
7βϕ[1]
(64-β)(192-β)
LHS[β]=ParametricFunction
Expression: ϕ
Parameters: {β,Λ}
[β,5][1]ϕ1p[1,β,Λm]=ParametricFunction
Expression: ϕ
Parameters: {β,Λ}
[β,5][1]
LHS1b[β]=ParametricFunction
Expression:
∂
β
ϕ
Parameters: {β,Λ}
[β,5][1]ϕ1p1b[1,β,Λm]=ParametricFunction
Expression:
∂
β
ϕ
Parameters: {β,Λ}
[β,5][1]
LHS1b[βm]=-0.185182ϕ1p1b[1,βm,Λm]=-0.185182
LHS1z[β]=
′
ParametricFunction
Expression: ϕ
Parameters: {β,Λ}
[β,5]
[z]ϕ1p1z[z,β,Λm]=
′
ParametricFunction
Expression: ϕ
Parameters: {β,Λ}
[β,5]
[z]
LHS1z[0.5,βm]=-0.0676282ϕ1p1z[0.5,βm,Λm]=-0.0676282
D[RHS[β],β]=-
7(192-2β)ϕ[1]
2(64-β)(384-β)
-
7(192-2β)βϕ[1]
2(64-β)
2
(384-β)
-
7(192-2β)βϕ[1]
2
2
(64-β)
(384-β)
+
7βϕ[1]
(64-β)(384-β)
BC1b[β,Km,Λm]=-
7(192-2β)ϕ[1]
2(64-β)(384-β)
-
7(192-2β)βϕ[1]
2(64-β)
2
(384-β)
-
7(192-2β)βϕ[1]
2
2
(64-β)
(384-β)
+
7βϕ[1]
(64-β)(384-β)
LHS[β]=ParametricFunction
Expression: ϕ
Parameters: {β,Λ}
[β,10][1]ϕ1p[1,β,Λm]=ParametricFunction
Expression: ϕ
Parameters: {β,Λ}
[β,10][1]
LHS1b[β]=ParametricFunction
Expression:
∂
β
ϕ
Parameters: {β,Λ}
[β,10][1]ϕ1p1b[1,β,Λm]=ParametricFunction
Expression:
∂
β
ϕ
Parameters: {β,Λ}
[β,10][1]
LHS1b[βm]=-0.0964062ϕ1p1b[1,βm,Λm]=-0.0964062
LHS1z[β]=
′
ParametricFunction
Expression: ϕ
Parameters: {β,Λ}
[β,10]
[z]ϕ1p1z[z,β,Λm]=
′
ParametricFunction
Expression: ϕ
Parameters: {β,Λ}
[β,10]
[z]