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

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






Therefore, the full expression for the derivative is