Solving Non-Linear Equations

Question

Shaumik 2012-10-15

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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);

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Answer 1

Rizwana Junaid 2012-10-15

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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.

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Shaumik 2012-10-15

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

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Answer 2

Walter Roberson 2012-10-15

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在 MATLAB Online 中打开

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

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Shaumik 2012-10-16

编辑：Shaumik 2012-10-16

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 2012-10-16