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

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Problem 1: Part 16: Newton iterations[edit]

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