Mathematics, 22.06.2019 20:20, lbelle

F(t, u) consider the following numerical method to solve u' = 1 un+1 = u" += (f\ + f2) , 2 where k is the time step, and fi f(t",u"), f2 = f(t" k, u" +kf\), (a) what is the order of local truncation error for the method? (b) what is the absolute stability region of this method? does it include the entire negative real axis? (c) take f(t, u) compute the solution up to the final time t = 1. verify the conclusion in (a) by your numerical results = -u +t with u(0) = 1.

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F(t, u) consider the following numerical method to solve u' = 1 un+1 = u" += (f\ + f2) , 2 where k i...