Nonlinear finite elements/Homework11/Solutions/Problem 1/Part 16

Problem 1: Part 16: Newton iterationsEdit

Let the nonlinear equations be  . Recall that the Newton method requires that we iterate using the formula

 

where   is the Newton iteration number. Derive an expression for the derivative of   that is required in the above formula.

Let us find the derivatives term by term. For the first term

 

For the second term

 

For the fourth term

 

For the third term

 

Now,

 

Similarly,

 

Therefore, the full expression for the derivative is