Dear seniors waiting for your response to my question

for reference please check the table. I am interested to draw table like this

@tomleslie  sir i admit I asked these questions

1-How can I generate this idea of perturbation theory on my question in maple by using for loop? means if we want to compare higher power of delta-like 2,3.... etc. 

2- how to test boundary conditionsNote on obtained solution u=u0+delta u1?

3- is it possible to compare this analytical solution numerical method?

I asked all these questions to generalized the problem that you produced in  pert2.mw.  

Note: you respond to all the above questions to the worksheet that upload for the reference point of view. But i am looking for the answer to my problem?

sorry

@tomleslie sir i appreciate your effort and it really looks like i want but the issue is that you made changes to the file that i attached for reference. I am trying the same procedure for my problem that you upload previously. Can you please help to extend the idea you did in #part3 on #part2? here is my original problem for which i a wondering and trying to get the solution.

My original worksheet

pert2.mw

@tomleslie sir really sorry, it was my fault. you were correct. it is working good and accordingly.  Sir my last query about this question.

1-How can I generate this idea of perturbation theory on my question in maple by using for loop? means if we want to compare higher power of delta-like 2,3.... etc. 

2- how to test boundary conditionsNote on obtained solution u=u0+delta u1?

3- is it possible to compare this analytical solution numerical method?

I am attaching a file for understanding which followed to solve my question.  In the attached file he or she used for loop for reference

sorry for inconvience

perturbation2.mw

Respected community waiting for your help in this regards

@tomleslie sir the obtained ODE after comparing the value of delta power 1 does not match with my manual calculation. 

first, I solved the nonlinear ode manually and he solves that (ode zero and first order) on maple and combined the solution in the form u=u0+deltau1 and then plot this solution for any fixed value of dp/dx and different values of delta...0.1..0.9. this is the main layout of my problem that I have done manually 

I am looking for a series of solutions to the problem. I have done it manually by using the method of perturbation method but now want to verify by using maple. let me show you my manual problem. do not want to solve directly means integration

not in maple sheet I used p=dp/dx and which will be considered as a constant. please have the problem formulation that i have done manually.

@tomleslie sir I am new to this maple and I am trying to understand and learning maple with how you wrote in the code. If I am an expert then no need to ask for help here. You helped me a lot to solve my problem but in the end make me disappointed rather than encouraging me to learn. you are most respectable because you teach and help me with my problem. After getting such insulting points still requested you for last help with my problem because I have a short time to submit it to my teacher and he is demanding i have to do in maple

I am interested to integrate p(x) over the domain x=0..1 and generate a table for different values of anyone parameter and kept another fix as you did for lambda.

@tomleslie sir thanks a lot now it is almost working according to my desire. Need graph and table for the following two points,

1- You have already ploted p/pmax versus x  that is ok, besides want to plot only for pmax versus k same as plotted in figure 4 in the pdf provided for refernce.

2- you asked about the integral of p(x) or p/pmax. I am interested to integrate p(x) over the domain x=0..1 and generate a table for different values any one parameter and kept other fix like you did for lambda.

Thank a lot for your help and awaiting your response about the above two points.

@tomleslie sir code working good and I apologize for an incomplete description of my problem. first, I want to clear that zeta is not involved in my problem I upload graphs and tables just for understanding and reference. In code can you please explain the purpose of the command  

1-

rhs(sol[j](0.5)[3])

2- How could i change my method from BVP to rk45?

3- here I am trying to explain my problem again.

I want to solve the given first order ode with mentioned boundary condition for the expression of p(x) then I need to plot p(x) for the different involved parameters.

2- want to calculate the expression and table for lambda for different values of involved parameters by fixing some and changes one.

3- next step is to find the maximum value of p(x) and the point where it is maximum then the plot for pmax?

4- At the last again want to integrate p(x) from 0 to 1 and generate a table for load for different values of the involved parameter.

 for reference, I am attaching a pdf file please look at equation numbers 32 and 33 and then figure 3 and 4 and table 1 and 2.

Note; The attached pdf for reference which explains the way I want to adopt it for my own problem calculation?

http://doi.org/10.1002/pen.25366 [Copyright material removed and replaced by link by moderator]

@tomleslie thanks sir, it is working good but I have few following observation

1- how can i change the method like rk45, Simpson 1/3, and trapezoid ?

2-I want to check the behaviour of the involved parameter by drawing the graph for different values of M {1,2,3..9} and by keeping other fix and then varying other and rest of the fixed. how could i do this? how could i do this combined or separately 

3- is it possible to get an expression for lambda in terms of involved parameter rather than numeric value? if not then how to draw a table for lambda for different values of the involved parameter. 

for more detail i am attaching two pictures please sir have to look on it and guide me about my requirement.