@roya2001 

no answer for this problem??

@Preben Alsholm 

hi .thanks Mr Preben Alsholm ....it is ture and you say correct.however how i can reform this boundary condition and gain answer..according your idea how we chose last approxsol for boundary condition (((D@@1)(g))(1)+(1/2)*((D@@1)(s))(1)^2 = 0)and determine omega??should we use another approach such as shooting method?

please use of latest file attached below...latest_file.mw

thanks a lot

@Preben Alsholm 

former version has been worked correctlly, but i want gain another answer in  approxsol for 

s(x)=cosh(upsilon*x)-cos(upsilon*x)-(cosh(upsilon)+cos(upsilon))*(sinh(upsilon*x)-sin(upsilon*x))/(sinh(upsilon)+sin(upsilon))

and 

g(x)=sin(((2*n+1)*(1/2))*Pi*x)

which have ploted in attached file.is there any way for answer?

thanks

plot.mw

Download plot.mw

@J4James 

amount of N is unknown....

@roya2001 

hi .i encounter another error in dsolve

please see and help

 ERROR.mw

thanks?

@torabi 

hi .i encounter another error in dsolve

please see and help

1)may i know that in code b=0 or b=1?

2)and line '' for b in extra_bcs do    try : print(b=1/(1)):.....

What role in calculationomega=30-mode2.mw

thanks?

@Preben Alsholm 

thanks.if we need to solve same equation, but including two unkown parameters (omerga 1 and oega2)

how we can two_unkown.mwsolve it?

thanks alot

@Preben Alsholm

thanks a lot. but i apply your comments in previous attached file. I think that you dont see  them after the loop....

@Preben Alsholm 

hi.thanks.in first question :how i can apply a change in program which result in a loop dos not appear?(this aim dos not result by changing ; to :) for example after loop 

''''''''''''''''''''''''

D(h2)(0) = 1
D(h2)(1) = 1
D(h4)(0) = 1
"initial Newton iteration is not converging"
D(h4)(1) = 1
"initial Newton iteration is not converging"
@@(D, 2)(h1)(0) = 1
"precision is insufficient for required absolute error, suggest

increasing Digits to approximately %1 for this problem", 22

                                  ...

'''''''''''''''''''''''''''''''''''''''''''''''''''''''''

How can the above results of solution do not show after loop. i.e (Blue lines)??
2)how i gain others omega2 such as 2.07982729632676 (*10^13) or 6.27005104177759 (*10^13),...which you say in previous comment?(I got 0.95... for all with guess omega2=1 and omega2= 2.33011874639388.

and 4.10059501931527 with guess omega2=2 ) but not gain 2.07982729632676 (*10^13) or 6.27005104177759 (*10^13)??
another_error.mw

@Preben Alsholm 

thanks a lot for your attention.please see following comments:

1)how i can apply a change in program which result in a loop dos not appear?(this aim dos not result by changing ; to :)

also according former your comment as 

''res[(D(h2))(1)](0); #Gives the eigenvalue found earlier 2.07982729632676 (*10^13)
res[(D(h2))(0)](0); #The same
res[((D@@2)(h1))(0)]; #omega2=6.27005104177759 (*10^13)
res[((D@@3)(h1))(0)]; #omega2= 12.5461315012613 (*10^13)''

i always gain omega2= .9562827793955890006 .how i gain others such as 2.07982729632676 (*10^13) or 6.27005104177759 (*10^13),...?

3)is gain always minimum omega2 by chosing omega2=1 in approxsoln?

thanks

@Preben Alsholm

thanks really.sorry i dont notice well....i reform program, but In the following

i Further encounter with some error which is searchable in attached file for finding another omega2 as eigenvalue?

please see and guide me.

thanks.another_error.mw

@Preben Alsholm 

thanks.but untill major avocation for me is encounter with error in attached file.

and second is gain another omega2 as eigenvalue?however you say about it in previous comment but i have problem with

thanksother_eignvlaue.mw

@Preben Alsholm 

yes i and farahnaz both work on same equation.

please help us.

@Preben Alsholm 

thanks.i uploaded worksheet here.also i cant gain another eigenvalues except omega2 = .95628277939558900063* 10 ^13   ...ERR0R.mw

@farahnaz 

hi.after many comment for this problem i fell  confused.

I don't quite understand which you say'' 

The loop now works on the system with scaled omega2.....''

i gain omega2 = .95628277939558900063 but for another eigenvalues  i could not find them...?

PLEASE type the requirment realations

ALSO

2) i want the selected function as h1(theta) and h2(theta) ,....have a solution with zeros only at the end points not in the interior of the interval? for example (maximum in middle of interval not zero)

3)in ''h1(theta) = theta*(1-theta), h2(theta) = sin(Pi*theta), h3(theta) = theta*(1-theta), h4(theta) = theta^2*(1-theta)^2'' who i change scale??multiple in 10^13???

please clarify

thanks..