@C_R 

Thanks can array table can be save as eps or jpeg format

@mmcdara 

i have fixed it still get the error: My problem is that i have an equation  W which constist of wo,w1,w2 and w3, where  wo ,w1 , w2 contain a ,b ,c  and a,b,c contains x1,x2,x3,x4 ( x1,x2,x3,x4 contain two types of data ) i want to plot the graphs for two data combine in one plot display in W,

@Rouben Rostamian  

Dear , i am unable to display the graphs of two data sets through a loop  . please see it where i am wrong. Thanks in advance.

Here i am attaching the worksheet.

Errors_in_display.mw

@Rouben Rostamian   

We are close to obtain the desire output, so should I do this attempt to plot the graph or leave it because of your help only  atleast I can able to get some results almost approaching to reach the goal.Shall I leave to plot or after some days again I have to attempt it, waiting for your  response and thanks for your patiently answer.But i  will be in disturb way untill I get the desire graphs.

@Rouben Rostamian  

As per your instructions i have fixed some errors but still i am unable to remove it.May be i am not able to write it in proper way. Please see it.I have attached sample graphs please see it 

1.The volumetric Flow rate is given by F= int(r . w, r = 0 .. h). 
w contain DP i want to plot the graph z=0..1 verses DP for different values of M=2,5,7

I have evaluated by  written w2 = int(r . w, r = 0 .. h) separately and i am facing difficulty to extract  DP from the w2 thats why i have written as F1:=F-w2, from there plot the graphs DP verses z for different values of M .

Because i am not expressing it proper way the graph of DP getting an output as inverted output.(where as i have used dp/dz=DP).

2. Wall shear stress is given by  Srz  = dw/dr at r  =h       
 
 i want to plot the graph z=0..1 verses  Srz for different values of M=2,5,7
 

3.The  Resistant impedance is given by  lambda= (1/ F) int(-DP, z = 0 .. L)  
contain DP i want to plot the graph delta=0..1 verses lambda for different values of M=2,5,7
Lambda:=(1/F)*int((-DP),zdz));   

Query-Comments3.mw

@Rouben Rostamian  

 I Have fixed but still error unable to resolve the issues. see the attached sheet

Query-Comments1.mw

@Rouben Rostamian  

Dear I am unable to evaluate the graphs please see the worksheet to help me

Query.mw

@Rouben Rostamian  

Thanks a lot

@Rouben Rostamian   Hear is the sheet.

Thanks a lot 

Two_data.mw

@Rouben Rostamian  

Dear i have try and got the result thanks  but  two times i have to run the codes to get the output. see i have written as per your suggestion for small changes in parameters 1 and parameters 2  i have written the codes as per your suggesion is that correct or we have to apply do or while loop to get the graphs. 

restart;
de1 := diff(w(r),r,r) + 1/r*diff(w(r),r) - (1/Da+x3/x1*M^2)*w(r) - 1/x1*(DP+theta(r)*x4*Gr*sin(alpha))=0:
de2 := diff(theta(r),r,r) + 1/r*diff(theta(r),r) + S/x5 = 0:
BCs1 := D(w)(0) = 0, w(h(z)) = 0:
BCs2 := D(theta)(0) = 0, theta(h(z))=0:
params1 :=
    DP=96*x1/(6-b*h(z)^2)/h(z)^4*(F + a*h(z)/24 - 11/6144*b*(b-4*a)*h(z)^8),
    a=x4*S*Gr/(4*x1*x5)*sin(alpha),
    b=1/Da+(x3*M/(x1*(1+m^2))),
    x1=1/((1-phi1)^(5/2)*(1-phi2)^(5/2)),
    x3=shnf/sf,
    x4=(1-phi2)*((1-phi1)+phi1*(RBs1)/(RBf))+phi2*RBs2/RBf,
    x5=khnf/kf,
    khnf=kbf*((ks2+2*kbf-2*phi2*(kbf-ks2))/(ks2+2*kbf+phi2*(kbf-ks2))),
    kbf=kf*((ks1+2*kf-2*phi1*(kf-ks1))/(ks1+2*kf+phi1*(kf-ks1))),
    shnf=sbf*((ss2+2*sbf-2*phi2*(sbf-ss2))/(ss2+2*sbf+phi2*(sbf-ss2))),
    sbf=sf*((ss1+2*sf-2*phi1*(sf-ss1))/(ss1+2*sf+phi1*(sf-ss1))),
    ks1=401, ks2=76.5, kf=0.4972,
    Da=1/10, Gr=2, S=1/10, alpha=Pi/4,
    m=1/2, F=3/2,
    RBs1=8933*16.7*10^(6),
    RBs2=6320*18*10^(6),
    RBf=1063*1.8*10^(6),
    ss1=59.6*10^(6),
    ss2=2.7*10^(-8),
    sf=6.67*10^(-1),
    phi1=1/100, phi2=2/100:

dsolve({de1,de2, BCs1, BCs2}, {w(r), theta(r)});

theta_sol := evalf(dsolve({subs(params1, de2), D(theta)(0)=0, theta(h(z)) = 0})):
We substitute the calculated theta into de1 and solve it for w:
evalf(subs(params1, theta_sol, de1)):
w_sol := evalf(dsolve({%, D(w)(0) = 0, w(h(z)) = 0})):
h := proc(z)
    local L, delta, d1, d2;
    L := 0.4:
    delta := 0.1:
    d1 := 0.3:
    d2 := 0.3: 
    return piecewise( z<=d1,   1,
        z<=d1+L,   1-(delta/(2))*(1 + cos((2*(Pi)/L)*(z - d1 - L/2))), 
        z<=d1+L+d2,  1 ):
end proc:
z := 1;
seq(rhs(w_sol), M in sqrt~([2, 5, 7 ,9])):

                                     
my_plot_1 := plot([%], r=0..h(z), color=["Red", "Green", "Blue", "Cyan"], linestyle=solid);
   params2 :=
    DP=96*x1/(6-b*h(z)^2)/h(z)^4*(F + a*h(z)/24 - 11/6144*b*(b-4*a)*h(z)^8),
    a=x4*S*Gr/(4*x1*x5)*sin(alpha),
    b=1/Da+(x3*M/(x1*(1+m^2))),
    x1=1/((1-phi1)^(5/2)*(1-phi2)^(5/2)),
    x3=shnf/sf,
    x4=(1-phi2)*((1-phi1)+phi1*(RBs1)/(RBf))+phi2*RBs2/RBf,
    x5=khnf/kf,
    khnf=kbf*((ks2+2*kbf-2*phi2*(kbf-ks2))/(ks2+2*kbf+phi2*(kbf-ks2))),
    kbf=kf*((ks1+2*kf-2*phi1*(kf-ks1))/(ks1+2*kf+phi1*(kf-ks1))),
    shnf=sbf*((ss2+2*sbf-2*phi2*(sbf-ss2))/(ss2+2*sbf+phi2*(sbf-ss2))),
    sbf=sf*((ss1+2*sf-2*phi1*(sf-ss1))/(ss1+2*sf+phi1*(sf-ss1))),
    ks1=401, ks2=76.5, kf=0.4972,
    Da=1/10, Gr=2, S=1/10, alpha=Pi/4,
    m=1/2, F=3/2,
    RBs1=893,
    RBs2=63,
    RBf=10*1.8,
    ss1=59.6,
    ss2=2.7*10,
    sf=6.67,
    phi1=1/100, phi2=2/100:
theta_sol := evalf(dsolve({subs(params2, de2), D(theta)(0)=0, theta(h(z)) = 0})):
evalf(subs(params2, theta_sol, de1)):
w_sol := evalf(dsolve({%, D(w)(0) = 0, w(h(z)) = 0})):
h := proc(z)
    local L, delta, d1, d2;
    L := 0.4:
    delta := 0.1:
    d1 := 0.3:
    d2 := 0.3: 
    return piecewise( z<=d1,   1,
        z<=d1+L,   1-(delta/(2))*(1 + cos((2*(Pi)/L)*(z - d1 - L/2))), 
        z<=d1+L+d2,  1 ):
end proc:
z := 1;
seq(rhs(w_sol), M in sqrt~([2, 5, 7 ,9])):
                                     
my_plot_2 := plot([%], r=0..h(z), color=["Red", "Green", "Blue", "Cyan"], linestyle=dash);
   
plots:-display(my_plot_1, my_plot_2);
 

@Rouben Rostamian

For first data set i have to run seprate codes and second data i have to write seprate then superimposed the two . the dummy like this i have to do:

de1 := ....
de2 := ....
BCs1 := ----
 
BCs2 :=....     
params1 :=
       .........
        RBs1=8933*16.7*10^(6),
        RBs2=6320*18*10^(6),
        RBf=1063*1.8*10^(6),
        ss1=59.6*10^(6),
        ss2=2.7*10^(-8),
        sf=6.67*10^(-1),
        
dsolve({de1,de2, BCs1, BCs2}, {w(r), theta(r)});     
theta_sol := evalf(dsolve({subs(params1, de2), D(theta)(0)=0, theta(h) = 0}));

theta(r) = -0.2289404327e-1*r^2+0.2289404327e-1*h^2

evalf(subs(params1, theta_sol, de1)):
w_sol := evalf(dsolve({%, D(w)(0) = 0, w(h) = 0}));

h := 1;
seq(rhs(w_sol), M in [2, 5, 7,9]):
my plot 1:=plot([%], r=0..h);
h := 'h':

then again i have to do like this

params2 :=
       .........
       RBs1=8933*16.7,

         RBs2=6320*18*10^(-6), 

        RBf=1000*1.8*10^(-2),
        ss1=59.6*10^(-2), 

        ss2=2.7*10^(-1), 

        sf=6.67*10^(3)

dsolve({de1,de2, BCs1, BCs2}, {w(r), theta(r)});     
theta_sol := evalf(dsolve({subs(params2, de2), D(theta)(0)=0, theta(h) = 0}));

theta(r) = -0.2289404327e-1*r^2+0.2289404327e-1*h^2

evalf(subs(params2, theta_sol, de1)):
w_sol := evalf(dsolve({%, D(w)(0) = 0, w(h) = 0}));

h := 1;
seq(rhs(w_sol), M in [2, 5, 7,9]):
my plot 2:=plot([%], r=0..h);

plots:-display(my_plot_1, my_plot_2);

@Rouben Rostamian

For the above codes  one data set is  { RBs1=8933*16.7*10^(6),         RBs2=6320*18*10^(6),         RBf=1063*1.8*10^(6),
        ss1=59.6*10^(6),         ss2=2.7*10^(-8),         sf=6.67*10^(-1),} and For the above codes   M  as [2, 5, 7,9]  we get the desire output as you have me  and again

for the second data set as   { RBs1=8933*16.7,         RBs2=6320*18*10^(-6),         RBf=1000*1.8*10^(-2),
        ss1=59.6*10^(-2),         ss2=2.7*10^(-1),         sf=6.67*10^(3),}  for the same we have to plot the graphs in that only but for this  line style should be different. Help me to get the desire sample graph .

@Rouben Rostamian  

By seeing the  maple prime question  on https://www.mapleprimes.com/questions/223044-Homotopy-Perturbation-Method

 by seeing the answer given by " Adjustment 

Answered: Kitonum 20374 "

i am trying to find how we can code in maple  to find w0,w1..... that's why i am trying to find

@Rouben Rostamian  

 Dear 

My purpose is to calculate the approximate solutions w0,w1, w2 ,w3 which is given in the article . I want to use Maple to find those values which is given in article

@Rouben Rostamian  

Thanks for observing carefully. 

I am looking for an asymptoic expansion in terms of the parameter and  the initial guess as  (r^2 - h^2)/4. I am seeing this equations and try to find using maple