@Rouben Rostamian  

this equations are algebric.should we use another approach such as newton instead Determinant??

in attached file below i encounter with error??

please chck it..

thanka

1.mw

@vv 

how i can solve this equation with Newton rule for Polynomial?? i think due to difference between component in matrix ,error was occured..

@acer

please see attached file

 determinan.mw

@iman 

is there answer for this equations?

@Preben Alsholm 

apply comments but i dont know how solve by existence unknown paramete such as (N)rmaple_prime.mw

Download maple_prime.mw

@Preben Alsholm 

I'm really sorry, But  I really not work on this pdsolve method. I Somewhat apply your these commands on attached file below, but i Faced with error''

Error, (in pdsolve/numeric/process_IBCs) initial/boundary conditions can only contain derivatives which are normal to the boundary, got (D@@(2[1](w)))(x, -1/6)

''

thus i Impotently want to help me .thanks alot

final_error.mw

                                                               program #1:primary

restart; Digits := 10; L := 1; h := 1/3; dsys3 := {diff(Phi(x, z), x, x)+diff(Phi(x, z), z, z) = 0, (2*(diff(u(x), x)+(1/2)*(diff(w(x), x))^2))*(diff(w(x), x, x))-4*(diff(w(x), x, x, x, x))+2*(diff(Phi(x, (1/2)*h), x, x))-2*(diff(Phi(x, (-h)*(1/2)), x, x))+2 = 0, diff(2*(diff(u(x), x)+(1/2)*(diff(w(x), x))^2), x) = 0}; IBC3 := {diff(Phi(x, (1/2)*h), z)+2*(diff(w(x), x, x)) = 0, diff(Phi(x, (-h)*(1/2)), z)+2*(diff(w(x), x, x)) = 0, -7*(diff(w(0), x, x))+2*(Phi(0, (1/2)*h)-Phi(0, (-h)*(1/2))) = 0, -7*(diff(w(L), x, x))+2*(Phi(L, (1/2)*h)-Phi(L, (-h)*(1/2))) = 0, Phi(0, z) = 0, Phi(L, z) = 0, u(0) = 0, u(L) = 0, w(0) = 0, w(L) = 0}

pdsolve(dsys3, IBC3, type = numeric)

                                                     program #2: modified above code as:

restart; Digits := 10; L := 1; h := 1/3; dsys3 := {diff(Phi(x, z), x, x)+diff(Phi(x, z), z, z) = 0, (2*(diff(u(x, z), x)+(1/2)*(diff(w(x, z), x))^2))*(diff(w(x, z), x, x))-4*(diff(w(x, z), x, x, x, x))+2*(diff(Phi(x, (1/2)*h), x, x))-2*(diff(Phi(x, (-h)*(1/2)), x, x))+2 = 0, diff(2*(diff(u(x, z), x)+(1/2)*(diff(w(x, z), x))^2), x) = 0}; IBC3 := {(D[2](Phi))(x, (1/2)*h)+2*(D@@2[1](w))(x, -(1/2)*h) = 0, (D[2](Phi))(x, (1/2)*h)+2*(D@@2[1](w))(x, (1/2)*h) = 0, -7*(D@@2[1](w))(0, z)+2*(Phi(0, (1/2)*h)-Phi(0, (-h)*(1/2))) = 0, -7*(D@@2[1](w))(L, z)+2*(Phi(L, (1/2)*h)-Phi(L, (-h)*(1/2))) = 0, Phi(0, z) = 0, Phi(L, z) = 0, u(0, z) = 0, u(L, z) = 0, w(0, z) = 0, w(L, z) = 0}

@Preben Alsholm

please apply your comment in maple file that attached before.i apply those in maple file and again accost with errors

thanks alot

@iman 

Hi everyone.

I have been experiencing a problem trying to solve a coupled system of 3 differencial equations

My problem is that a got a message back as I try to solve the system:

"Error, (in pdsolve/numeric/process_IBCs) improper op or subscript selector"

by apply this point that ''all dependent variables must be functions of the same independent variables''

i again accost with another error ''

Error, (in pdsolve/numeric/process_IBCs) initial/boundary conditions can only contain derivatives which are normal to the boundary, got (D[1, 1](w))(x, -3/400000000)

''

please help me.....very very thankserror_pdsolve.mw

@Axel Vogt 

I'm so sorry.

i dont understand good your answer.sorry .please please explain with Full details

thanks a lot....

@Axel Vogt 

thanks for good answer, but i have  questions of you

1)why at the end of calculation, end limit of phi is pi/2????

2)i dont understand your idea for ( theta <> k*Pi) and (d=ra) and  (D=d*sin(theta)) ,please more explain

thanks a lot.....