Question: (30 points) Given the equation u' = f(u) u(0) = uo and the numerical method un+1 u' - 1+ , Atf (un + 1 )

(30 points) Given the equation u' = f(u) u(0) = uo and the numerical method un+1 u' - 1+ , Atf (un + 1 ) (a) Write the LTE for this method, and using Taylor expansions, determine what the order of the LTE is. (b) Is this method a one-step method or a multi-step method? Explain. (c) State the Lax-Richtmeyer equivalence theorem and explain how it applies for this problem (d) Will this method be stable for the case u' = 0? Show work and explain

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