# Having problem in solving hyperbolic functions

I am trying to solve Upm/Um at different points but I am not getting any result. There is any problem with my hyperbolic function? Please help me to get the results. It will be appreciated.

t = 0.3; Da = 10^-4; ϵ = 0.9;
A1 = Da + t^2/2 -
Da Sech[((-1 + t) Sqrt[ϵ])/
Sqrt[Da]] - (Sqrt[
Da] t Tanh[((-1 + t) Sqrt[ϵ])/
Sqrt[Da]])/ϵ^(3/2);
A2 = (Sqrt[
Da] Sech[((-1 + t) Sqrt[ϵ])/
Sqrt[Da]] (-t Cosh[Sqrt[ϵ]/Sqrt[Da]] +
Sqrt[Da] ϵ^(3/2) Sinh[(t Sqrt[ϵ])/
Sqrt[Da]]))/ϵ^(3/2);
A3 = -((Sqrt[
Da] Sech[((-1 + t) Sqrt[ϵ])/
Sqrt[Da]] (Sqrt[
Da] ϵ^(3/2) Cosh[(t Sqrt[ϵ])/Sqrt[Da]] -
t Sinh[Sqrt[ϵ]/Sqrt[Da]]))/ϵ^(3/2));
Uc = -(Y^2/2) + A1;
Upm = A2*Sinh[(Y Sqrt[ϵ])/Sqrt[Da]] +
A3*Cosh[(Y Sqrt[ϵ])/Sqrt[Da]] + Da;
Um = FullSimplify[Integrate[Uc, {Y, 0, t}] + Integrate[Upm, {Y, t, 1}]]

pm = Table[{(Upm)/(Um)}, {Y, 0.3, 1, 0.01}]
(* 0.0100841 *)
(* {{0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, \
{0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, \
{0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, \
{0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, \
{0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, \
{0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, {0.}, \
{0.}, {0.}, {0.}, {0.}, {0.}, {0.}} *)


Clear["Global*"]

t = 3/10; Da = 10^-4; ϵ = 9/10;
A1 = Da + t^2/2 -
Da Sech[((-1 + t) Sqrt[ϵ])/
Sqrt[Da]] - (Sqrt[
Da] t Tanh[((-1 + t) Sqrt[ϵ])/
Sqrt[Da]])/ϵ^(3/2);
A2 = (Sqrt[
Da] Sech[((-1 + t) Sqrt[ϵ])/
Sqrt[Da]] (-t Cosh[Sqrt[ϵ]/Sqrt[Da]] +
Sqrt[Da] ϵ^(3/2) Sinh[(t Sqrt[ϵ])/
Sqrt[Da]]))/ϵ^(3/2);
A3 = -((Sqrt[
Da] Sech[((-1 + t) Sqrt[ϵ])/
Sqrt[Da]] (Sqrt[
Da] ϵ^(3/2) Cosh[(t Sqrt[ϵ])/Sqrt[Da]] -
t Sinh[Sqrt[ϵ]/Sqrt[Da]]))/ϵ^(3/2));
Uc = -(Y^2/2) + A1 // Simplify;
Upm = A2*Sinh[(Y Sqrt[ϵ])/Sqrt[Da]] +
A3*Cosh[(Y Sqrt[ϵ])/Sqrt[Da]] + Da // Simplify;

Um = Simplify[Integrate[Uc, {Y, 0, t}] +
Integrate[Upm, {Y, t, 1}]];


Tabulating

pm = Table[Upm/Um, {Y, .3, 1, 0.01}]

(* {0.354624, 0.143341, 0.0615222, 0.0298377, 0.0175679, 0.0128164, \
0.0109763, 0.0102638, 0.00998786, 0.009881, 0.00983962, 0.0098236, \
0.00981739, 0.00981499, 0.00981406, 0.0098137, 0.00981356, 0.0098135, \
0.00981348, 0.00981348, 0.00981347, 0.00981347, 0.00981347, \
0.00981347, 0.00981347, 0.00981347, 0.00981347, 0.00981347, \
0.00981347, 0.00981347, 0.00981347, 0.00981347, 0.00981347, \
0.00981347, 0.00981347, 0.00981347, 0.00981347, 0.00981347, \
0.00981347, 0.00981347, 0.00981347, 0.00981347, 0.00981347, \
0.00981347, 0.00981347, 0.00981347, 0.00981347, 0.00981347, \
0.00981347, 0.00981347, 0.00981347, 0.00981347, 0.00981347, \
0.00981347, 0.00981347, 0.00981346, 0.00981345, 0.00981343, \
0.00981336, 0.00981318, 0.00981273, 0.00981155, 0.00980851, \
0.00980065, 0.00978037, 0.00972801, 0.00959278, 0.00924357, \
0.00834181, 0.0060132, 0.} *)

• Thanks@Bob Hanlon for your help. I don't understand why I was not getting the results before. It seems that the equations are the same. Apr 20 '20 at 7:04
t = 0.3; Da = 10^-4; \[Epsilon] = 0.9;
A1[t_] :=
Da + t^2/2 -
Da Sech[((-1 + t) Sqrt[\[Epsilon]])/
Sqrt[Da]] - (Sqrt[
Da] t Tanh[((-1 + t) Sqrt[\[Epsilon]])/
Sqrt[Da]])/\[Epsilon]^(3/2);
A2[t_] := (Sqrt[
Da] Sech[((-1 + t) Sqrt[\[Epsilon]])/
Sqrt[Da]] (-t Cosh[Sqrt[\[Epsilon]]/Sqrt[Da]] +
Sqrt[Da] \[Epsilon]^(3/2) Sinh[(t Sqrt[\[Epsilon]])/
Sqrt[Da]]))/\[Epsilon]^(3/2);
A3[t_] := -((Sqrt[
Da] Sech[((-1 + t) Sqrt[\[Epsilon]])/
Sqrt[Da]] (Sqrt[
Da] \[Epsilon]^(3/2) Cosh[(t Sqrt[\[Epsilon]])/Sqrt[Da]] -
t Sinh[Sqrt[\[Epsilon]]/Sqrt[Da]]))/\[Epsilon]^(3/2));
Uc[Y_] := -(Y^2/2) + A1;
Upm[Y_] :=
A2*Sinh[(Y Sqrt[\[Epsilon]])/Sqrt[Da]] +
A3*Cosh[(Y Sqrt[\[Epsilon]])/Sqrt[Da]] + Da;
Um[Y_] = FullSimplify[
Integrate[Uc, {Y, 0, t}] + Integrate[Upm, {Y, t, 1}]]
pm = Table[{(Upm[Y])/(Um[Y])}, {Y, 0.3, 1, 0.01}]


[Out]

{{(1/10000 + 1.14606*10^12 A2 + 1.14606*10^12 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 2.95948*10^12 A2 + 2.95948*10^12 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 7.64229*10^12 A2 + 7.64229*10^12 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.97347*10^13 A2 + 1.97347*10^13 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 5.09612*10^13 A2 + 5.09612*10^13 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.31597*10^14 A2 + 1.31597*10^14 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 3.39825*10^14 A2 + 3.39825*10^14 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 8.77532*10^14 A2 + 8.77532*10^14 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 2.26606*10^15 A2 + 2.26606*10^15 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 5.85166*10^15 A2 + 5.85166*10^15 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.51108*10^16 A2 + 1.51108*10^16 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 3.90207*10^16 A2 + 3.90207*10^16 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.00763*10^17 A2 + 1.00763*10^17 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 2.60202*10^17 A2 + 2.60202*10^17 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 6.71922*10^17 A2 + 6.71922*10^17 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.73511*10^18 A2 + 1.73511*10^18 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 4.48058*10^18 A2 + 4.48058*10^18 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.15702*10^19 A2 + 1.15702*10^19 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 2.98779*10^19 A2 + 2.98779*10^19 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 7.71539*10^19 A2 + 7.71539*10^19 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.99235*10^20 A2 + 1.99235*10^20 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 5.14487*10^20 A2 + 5.14487*10^20 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.32856*10^21 A2 + 1.32856*10^21 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 3.43076*10^21 A2 + 3.43076*10^21 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 8.85927*10^21 A2 + 8.85927*10^21 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 2.28773*10^22 A2 + 2.28773*10^22 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 5.90763*10^22 A2 + 5.90763*10^22 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.52553*10^23 A2 + 1.52553*10^23 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 3.93939*10^23 A2 + 3.93939*10^23 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.01727*10^24 A2 + 1.01727*10^24 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 2.62691*10^24 A2 + 2.62691*10^24 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 6.78349*10^24 A2 + 6.78349*10^24 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.75171*10^25 A2 + 1.75171*10^25 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 4.52344*10^25 A2 + 4.52344*10^25 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.16809*10^26 A2 + 1.16809*10^26 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 3.01637*10^26 A2 + 3.01637*10^26 A3)/(
0.3 Uc + 0.7 Upm)}, {(1/10000 + 7.7892*10^26 A2 + 7.7892*10^26 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 2.01141*10^27 A2 + 2.01141*10^27 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 5.19408*10^27 A2 + 5.19408*10^27 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.34127*10^28 A2 + 1.34127*10^28 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 3.46357*10^28 A2 + 3.46357*10^28 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 8.94401*10^28 A2 + 8.94401*10^28 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 2.30962*10^29 A2 + 2.30962*10^29 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 5.96415*10^29 A2 + 5.96415*10^29 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.54013*10^30 A2 + 1.54013*10^30 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 3.97708*10^30 A2 + 3.97708*10^30 A3)/(
0.3 Uc + 0.7 Upm)}, {(1/10000 + 1.027*10^31 A2 + 1.027*10^31 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 2.65204*10^31 A2 + 2.65204*10^31 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 6.84838*10^31 A2 + 6.84838*10^31 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.76846*10^32 A2 + 1.76846*10^32 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 4.56671*10^32 A2 + 4.56671*10^32 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.17927*10^33 A2 + 1.17927*10^33 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 3.04523*10^33 A2 + 3.04523*10^33 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 7.86371*10^33 A2 + 7.86371*10^33 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 2.03065*10^34 A2 + 2.03065*10^34 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 5.24377*10^34 A2 + 5.24377*10^34 A3)/(
0.3 Uc + 0.7 Upm)}, {(1/10000 + 1.3541*10^35 A2 + 1.3541*10^35 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 3.49671*10^35 A2 + 3.49671*10^35 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 9.02957*10^35 A2 + 9.02957*10^35 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 2.33171*10^36 A2 + 2.33171*10^36 A3)/(
0.3 Uc + 0.7 Upm)}, {(1/10000 + 6.0212*10^36 A2 + 6.0212*10^36 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.55486*10^37 A2 + 1.55486*10^37 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 4.01512*10^37 A2 + 4.01512*10^37 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.03683*10^38 A2 + 1.03683*10^38 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 2.67741*10^38 A2 + 2.67741*10^38 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 6.91389*10^38 A2 + 6.91389*10^38 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.78538*10^39 A2 + 1.78538*10^39 A3)/(
0.3 Uc + 0.7 Upm)}, {(1/10000 + 4.6104*10^39 A2 + 4.6104*10^39 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 1.19055*10^40 A2 + 1.19055*10^40 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 3.07436*10^40 A2 + 3.07436*10^40 A3)/(
0.3 Uc + 0.7 Upm)}, {(
1/10000 + 7.93893*10^40 A2 + 7.93893*10^40 A3)/(0.3 Uc + 0.7 Upm)}}
`
• Actually I need the output in exact values. This one still depends on constant values. Apr 19 '20 at 19:59