# newton Raphson

• Oct 15th 2007, 09:28 PM
helmszee
newton Raphson

write out the formula for newton raphson metho applied to this equation tabulat successive values of netwon raphson approximation for this equation, with starting solution x = 1 untill u have the root to at least 5 deciamal places..

..ahh help!?

formula

x - f(x)/f'(x) right?

so

1 - 1.1x^1.4 - cosx / 1.54x^.4 + sinx .......... ? right?

then what??
• Oct 15th 2007, 10:31 PM
ticbol
formula

x - f(x)/f'(x) right?

so

1 - 1.1x^1.4 - cosx / 1.54x^.4 + sinx .......... ? right?

then what??

The "formula" is
x2 = x1 -[f(x1) / f'(x1)]
x3 = x2 -[f(x2) / f'(x2)]
and so on....

where
x1, x2, x3 are read x sub 1, x sub 2, x sub 3, respectively.

x2 is nearer to the correct root than x1.
x3 is nearer to the correct root than x2.
and so on...

x2 = x1 -[(1.1(x1)^(1.4) -cos(x1)) / (1.54(x1)^(0.4) +sin(x1))]

{Too many parentheses and brackets? Yes. You need to practice that. :)}

Then just substitute the seed root, or starting solution, x1 = 1 in the formula to get x2.
x2 = 1 -[(1.1(1)^(1.4) -cos(1)) / (1.54(1)^(0.4) +sin(1))]

{In the cos(1) and sin(1), the 1 is 1 radian. So use your calculator's angle mode in radians.}
x2 = 1 -[(1.1(1) -0.540302306) / (1.54(1) +0.841470985)]
x2 = 1 -0.235021841
x2 = 0.764978159

Then, for the second iteration,
x3 = 0.764978159 -[(1.1(0.764978159)^(1.4) -cos(0.764978159)) / (1.54(0.764978159)^(0.4) +sin(0.764978159))]

Whoa, if you can navigate that, you are good.

Go up to x4 or x5 or x6, if you like.
{Normally, if x1 is close enough to the correct solution, you need up to x4 only.}
• Oct 15th 2007, 10:43 PM
CaptainBlack
Quote:

Originally Posted by helmszee

write out the formula for newton raphson metho applied to this equation tabulat successive values of netwon raphson approximation for this equation, with starting solution x = 1 untill u have the root to at least 5 deciamal places..

..ahh help!?

formula

x - f(x)/f'(x) right?

$
x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}
$

Quote:

so

1 - 1.1x^1.4 - cosx / 1.54x^.4 + sinx .......... ? right?

then what??

$
f(x)=1.1 x^{1.4}-\cos(x)
$

So the N-R itteration is:

$
x_{n+1}=x_n-\frac{1.1 x_n^{1.4}-\cos(x_n)}{1.54 x_n^{0.4}+\sin(x_n)}
$

Now you need an initial guess at a root try $x_0=0.5$ or $x_0=0.7$, and away you go.

RonL