@Preben Alsholm 

I want to thank you for preparing these equations . I always exhaust you with asking unusual questions

Thanks

@Kitonum 

Thanks for your suggestion ... I want to extract function of phi(x) and psi(x) ,,, the second case : it is importat to note that it is a linear coupled equation ... I think that it must have a analytically solution ... thanks

I forgot to type some constants :

a:=1.62338:
sigma1:=1.93251*10^7:
sigma2:=9.99998*10^7:
thank you very much for your helps

@Preben Alsholm 

Thanks all

thanks for your help guys. maple is my love

@Kitonum 

Thank you very much

I'm sure that without your help, I couldnt achieve it.

best regards

@Carl Love 

Many thanks for your help but my problem havent been solved by this method.

Indeed, my problem is something like this :

Ugen := .1049253920*phi(x)^2+.2490325160*psi(x)^2+0.7218836157e-1*eta(x)^2+0.4163942054e-1*(diff(psi(x), x))^2+0.3590610475e-1*(diff(phi(x), x))^2+0.1916547983e-2*psi(x)*(diff(phi(x), x, x))+0.5733315777e-2*(diff(psi(x), x))*(diff(phi(x), x))-0.3273703041e-1*phi(x)*psi(x)-0.3273703035e-1*psi(x)*eta(x)+0.4980952543e-2*(diff(phi(x), x, x))^2-0.7191876251e-1*phi(x)*eta(x)+0.1153177175e-2*eta(x)*(diff(phi(x), x, x))+0.1073591707e-1*phi(x)*(diff(phi(x), x, x))


now when I use your code the answer is:

{}

not the coefficients.

@Preben Alsholm 

You do it good without my explanation but it has some problem that it must be solved before. I want to explain it better .It's a coupled equation that has boundary values.

The boundary conditions are:
phi(a)=sigma01,phi(-a)=sigma01,D(phi)(a)=0,D(phi)(-a)=0,psi(a)=sigma02,psi(-a)=sigma02
but you think that this code has boundary values like this : phi(a)=1,phi(-a)=1 that is wrong.

The second point that I have to add in this part is that about b11,b12,b21,b22

When we have a relation in matrix form.look at the below.I try to explain my relation in maple form:

j1:=matrix([[diff(phi(xi),xi,xi,xi)],[diff(psi(xi),xi)]]):

DD:=matrix([[b11,b12],[b21,b22]]):

sig:=matrix([[sigma01],[sigma02]]):

j1:=multiply(DD,sig):

I want to arrive phi and psi with sigma01 and sigma02 to have j1 .

Now with these explanations I think that we must change res1 but when I use sigma01 instead of 1 in above boundary condition . I cant do and this give me error .

What should I do?

@Preben Alsholm 

I'm waiting for your answer after upload my file

@Preben Alsholm 

sorry about D in analytically method .it must be DD := Matrix(2, 2, {(1, 1) = -3.44593215675164, (1, 2) = .513011296033875, (2, 1) = -.101647391754337, (2, 2) = 1.47853652998948}).

but in above comment , I wrote down the numerical answer.

@Preben Alsholm 

Thanks alot.
It's the numerical method that you had talked about.

In analytically method for c=0.1 , DD is :
DD := Matrix(2, 2, {(1, 1) = -52.51404320-0.5320000000e-7*I, (1, 2) = 130.1308952-0.8274715690e-8*I, (2, 1) = 21.93016296-0.6740000000e-7*I, (2, 2) = 157.7727024-0.9938248060e-8*I})

But in numerical method that I upload in this comment , I have another measure.

Of course I want to say this point when I use c=4 , this numerical is the same measure that numerical has.But for c between 0to1 I have many error in numerical method. please solve my problem .thanks alot

ta_solve1.mw

@Preben Alsholm 
please leave your email address for me to send you some maple files that help you to understand what I mean.

My explanation is that we have  numerical and analytical methods for this coupled differention equation.

In analytically method that it has the accurately answer for us, we arrive to a measure for phi and psi and after that we use these functions in another matrices for determination a variable. You have seen file-1 charts. In this chart you can see different measures for x in this method .

when we use numerical and analytical methods . we has a difference between them . In file-1 you can see this difference between numerically and analytically methods for that variable.

Generally my question in this part is that:

We know this reality that numerical method has a few error always.How can we decrease these errors?

best the wishes

Thanks my friend for your help.

About the second boundary condition , you're right. it was eval(PSI,x=-1.366)=1
But my question in this post is that how I can improve my results in nummerical methods?

you know that analytically methods have the best results generally but sometimes we need do some numerical methods for getting result faster.

This coupled differentional equation has an another solution.

I use phi and psi after solve in some matrices that have a shape in file1.

When I want to use nummerical method,I have a problem in shape of this results.

see this comparison.

please help me that how I can improve my results?
someone told me something about using loop in these methods but I dont know anything about this numerical method.

thanks alot my friend preben

file-1.xlsx

@Preben Alsholm 

thanks alot 

you're one of my  best friends that i have ..

i love you ...

i find it easy with your skill ... 

i'm really glad to know you man ...

be success 

@Preben Alsholm 

thanks alot preben for your help

without your help , i couldnt do anything

now I want to solve it analytically in one reason that i'll explian it later...

consider these equations:

VR22:=0.1178*diff(phi(x),x,x,x,x)-0.2167*diff(phi(x),x,x)+0.0156*diff(psi(x),x,x)+0.2852*phi(x)+0.0804*psi(x):
VS22:=0.3668*diff(psi(x),x,x)-0.0156*diff(phi(x),x,x)-0.8043*psi(x)-0.80400*phi(x):
bok:=evalf(dsolve([VR22=0,VS22=0],{phi(x),psi(x)}));

I have the same boundary conditons

As you see in these equations, we need only six boundary conditions (because of differention equation order 4th and 2th)

but in my answer in this equation , i have 12 coefficients which are belonged to phi(x) and psi(x)...

I'm looking for a solution of these linear differential eqs.

i want to see the functions phi(x) and psi(x) ... because i want to know about their differentions for example phi'(x) ... and phi''(x) and psi'(x) ...

In numerically method ... I saw only shapes of these function ... but i want to see these functions parametric

for example phi(x)= 2*x+1. I want responds from these equations parametric ...

... thanks alot for your help ...

@Preben Alsholm 

thanks Preben Alsholm ...

but how can i solve it in numerical methods?

I'm really interested in solving this equation