I deduced my silly formula when in bed yesterday to help me sleep. And to verify it, I replaced 'a' with 30 deg. So when I found out it is ok (bad luck), I had a good sleep
Next day, I didn't bother myself to check it more carefully since I used having confidence in my brain. But I should remember from now on that I am not young anymore at age 64
Thank you again for pointing out my silly mistake here.
I wished that Cannibol found it first.
Knowing for sure that something is wrong is a good sign for one's ability in finding the right answer.
Now, assume you have the initial values of Q1 and Q2.
Now substitute the initial value of Q2 in the first equation and obtain Q1.
The obtained value of Q1 is put into the 2nd equation to obtain Q2.
This completes the 1st iteration.
Now again re-substitute the obtained values (new) of Q1 and Q2 into the above equations to obtain 2 new solutions for Q1 and Q2. This completes the 2nd iteration.
Keep on iterating until the values of Q1 and Q2 become stable, by which I mean they don't change anymore. This is the final solution for Q1 and Q2.
I have tried it out and the answer is coming to be the exact one as mentioned in the text book.
Phew!
CASE CLOSED, PROBLEM SOLVED!
But still I am keeping this thread open, as one day maybe someone comes up with a unique way to solve it. Who knows?
Do you say, your textbook already stated that the equations can't be analytically solved?
I had guessed this, too. But once you decide for an iterative (= numerical) solution, it's just number crunching. Finding good start values is helpful but not necessarily required.
Unless you proof it, you can't be sure it converges for any value of the parameters.
Do you say, your textbook already stated that the equations can't be analytically solved?
I had guessed this, too. But once you decide for an iterative (= numerical) solution, it's just number crunching. Finding good start values is helpful but not necessarily required.
Most likely it doesn't converge for arbitrary parameter combinations.
Yes, I think you are right! It may not converge for arbitrary values, which I remember from my old experiences learning "numerical analysis" as a subject in my graduate days.
Actually, there are a pair of equations that gives you the initial values of Q1 and Q2, which I forgot to tell you. Sorry, I am an amateur naa... forgive me, MY MISTAKE!!!
Saying that, I thought it wouldn't help to solve the above equations.
Anyways, thank you all for bearing with a stupid like me.