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Suppose that Euler's, Heun, or the RK4 method is applied to an IVP dy dt = f(t, y), y(to) = yo which has exact solution
Suppose that Euler's, Heun, or the RK4 method is applied to an IVP dy dt = f(t, y), y(to) = yo which has exact solution y = $(t). [HINT: Maple Exploration MMT.ME3.4.1 may be helpful.] a. The accuracy of Euler's Method is independent of the curvature of o(t). b. Reducing the size of the stepsize h always reduces the error in the approximation. c. If the local error en is proportional to h" for stepsize h, then we say the method is of order p. d. Either of the Heun or RK4 methods will give a better approximation to the solution than Euler's Method because in those methods, each step uses more information about the direction field. e. None of the above
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