Solving Non-Linear Equations

I am stuck up with the following program. I want to solve for 3 variables b, n, k. Please help.

for b,n,k I am getting <1x1 sym> how to get the values? Any help would be highly apprecaited.. Thanks

clear

T = 0.89;
R = 0.11;
lamda = 0.98;
d = 1.65;
pi = 3.14;
phit = 0.60;
phir = 0.31;

syms  b n k;

eq1 = 'phir=atan(((-2)*k)/(1-((n)^2)-((k)^2)))';

eq2 = 'T=((1-R)^2)+((4)*(R)*(sin(phir)^2))*(exp((-((4*(pi)*k)/(lamda)))*(d)))/((1)-(R)*(exp(((4*(pi)*k)/(lamda))*(d)))^2)+((4)*(R)*(exp(((4*(pi)*k)/(lamda))*(d)))*(sin(b+phir)^2))';

eq3 = 'phit=((2)*(pi)*(n)*(d)/(lamda))+arctan(((k)*((n)^2+(k)^2-(1)))/(((k)^2+(n)^2)*(2+n)*(n)))+arctan((((R)*exp((4)*(pi)*(k))/(lamda))*(sin(b+phir)^2))/((1)-((R)*exp((4)*(pi)*(k)))/(lamda))*(cos(b+phir)^2))';

eq4 = 'b=(((2)*(pi)*(n)*(d))/(lamda))';

sol1 = solve(eq1);
sol2 = solve(eq2);
sol3 = solve(eq3);
sol4 = solve(eq4);

Answer 1

[Rizwana Junaid]

you can solve ur system by calling ode45 function. for that you will have to save all equations in one file and call the solver function from the other main file.

[Shaumik]

Thanks Junaid. But my non-linear equations are not in the differential form. So will ode45 work?

I am new to MATLAB and got stuck for a long time with this. Please suggest

Answer 2

[Walter Roberson]

You need to remove all of your apostrophes. If you are using R2012a or later, change your = that are in the equations to == but if you are using an earlier version, convert your A=B forms to (B)-(A) or (A)-(B) with no = or == in the definition of the expression. For example,

eq4 = (b)-((((2)*(pi)*(n)*(d))/(lamda)));

The result of your solve() is going to be a structure array with one field for each variable name. Access the field to see the value, such as

sol4.k

[Shaumik]

Thanks Walter. I am using R2012a, and changed accordingly.

But got the error.

??? Undefined function or method 'arctan' for input arguments of type 'sym'.

eq3=phit==((2)*(pi)*(n)*(d)/(lamda))+(arctan(((k)*((n)^2+(k)^2-(1)))/(((k)^2+(n)^2)*(2+n)*(n))))+(arctan((((R)*exp((4)*(pi)*(k))/(lamda))*(sin((((2)*(pi)*(n)*(d))/(lamda))+phir)^2))/((1)-((R)*exp((4)*(pi)*(k)))/(lamda))*(cos((((2)*(pi)*(n)*(d))/(lamda))+phir)^2)));

[Shaumik]

Thanks Walter.. I am still getting some other errors now :( I am confused about where I'm going wrong. Is my approach correct?

Answer 3

[Sachin Ganjare]

Undefined function or method 'arctan' for input arguments of type 'sym'.

Matlab function name is 'atan' and not 'arctan'

Hope it helps!!!

[Shaumik]

Thanks Sachin. I dont know how I made the error.

Anyways...is the process correct for solving non-linear equations? I am still getting the errors:

??? Error using ==> char Conversion to char from logical is not possible.

Error in ==> solve>getEqns at 169 vc = char(v);

Error in ==> solve at 67 [eqns,vars] = getEqns(varargin{:});

Error in ==> RI at 21 sol1=solve(eq1);

Please help..

[Sachin Ganjare]

Probably you do not need quotes in your equation.

Check in your version of matlab documentation.

Hope it helps!!!

[Shaumik]

Yes, I removed the quotes as well (version is R2012a). I replaced the = sign with == as well.