Consider the differential equation y = f (t, y), a t b, y(a) = . a. Show that y (ti) =
Chapter 5, Problem 5.10.4(choose chapter or problem)
Consider the differential equation y = f (t, y), a t b, y(a) = . a. Show that y (ti) = 3y(ti) + 4y(ti+1) y(ti+2) 2h + h2 3 y(1), for some , where ti < i < ti+2. b. Part (a) suggests the difference method wi+2 = 4wi+1 3wi 2h f (ti, wi), for i = 0, 1,... , N 2. Use this method to solve y = 1 y, 0 t 1, y(0) = 0, with h = 0.1. Use the starting values w0 = 0 and w1 = y(t1) = 1 e0.1. c. Repeat part (b) with h = 0.01 and w1 = 1 e0.01. d. Analyze this method for consistency, stability, and convergence.
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