help needed understanding basics of solving non linear equations using newtons method

hi guys..

I have problem in combustion kinetics which requires solving four non-linear equations with 7variables. I have reduced the number of variables to 4 but am not sure how to solve this using the newton raphson method... could someone help me by illustrating the method with a detailed example...

i am trying to solve the equations in matlab.

captain black had posted this:

First find the Jacobian:

Now Newton's method proceeds from a initial approximation of guess: to the next approximation using by solving:

for , then the next estimate is:

.

Then the general itteration step is:

solve:

for , then the next estimate is:

.

In Matlab the equation J dP= P is solved using a statement of the form:

dP=J\P

if I recall correctly

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my difficulty lies in understanding how the iteration process proceeds.... also

could some one illustrate this with an example...

my equations are

F=[m*(0.0588-x(1,1))-(6.19*10^9*exp((-15098)./x(4,1)))*30*0.0021*(101325/(8314*x(4,1))).^1.75*x(1,1).^0.1*(0.233*x(2,1)).^1 .65;

m*(0.9412-x(2,1))-(4.76/3.5)*(6.19*10^9*exp((-15098)/x(4,1)))*30*0.0021*(101325/(8314*x(4,1))).^1.75*x(1,1).^0.1*(0.233*x(2,1)).^1 .65;

1-x(1,1)-x(2,1)-x(3,1);

x(1,1)*(-84.667)+x(3,1)*(-241.845)-0.0588*(-84.667)-0.9412+32*(x(4,1)-298)

];

here i need to find x(:,1) as m varies from 0 to 0.2 and plot a graph of m vs x

thanks to anyone who is willing to go the way...