How to solve iteratively equation

I hava next equation

p0=sqrt(1+64*beta)

p=p0+8*(1/p0-1)

and i need to solve it for beta where I have exact value for p. How can I do it iteratively or on some other way in Matlab?

[Stephan]

Hi Jan,

see my answer below to get a solution to your problem. I saw that you got some answers on your questions here in the forum. Did you notice that you can accept and/or vote for useful answers? This is the easiest way to thank the volunteers here for their help.

Answer 1

[Stephan]

Hi,

there is an analytic solution:

syms p0 p beta
eqn1 = p0 == sqrt(1+64*beta);
eqn2 = p == p0+8*(1/p0-1);
eqn2 = subs(eqn2,p0,rhs(eqn1));
% analytic solution
sol = isolate(eqn2,beta);
% function handle for numeric calculations
fun = matlabFunction(rhs(sol));
% assume a value (or vector of values for p)
p_exact = [2.5 5 10];
% get numeric results
result = fun(p_exact)

In case you do not have access to the Symbolic Math Toolbox, here is the function handle to calculate beta from known p-values:

fun = @(p)1.0./(p./1.6e1+sqrt(p.*1.6e1+p.^2+3.2e1)./1.6e1+1.0./2.0).^2./6.4e1-1.0./6.4e1

Best regards

Stephan