The numerical result from this process is the sequence uº, u', u², ..., which can be interpreted as an approximation to the exact solution sampled at times 0, delta t,2 delta t, . .. (a) If g(u) is a general nonlinear function and is differentiable, write down an iteration which determines un+1 from Newton's method. (b) The convergence of Newton's method depends on the choice of the initial guess. What would be a sensible choice for an initial guess?
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