Consider the initial value problem y(1) = 2. y' = 1 + 1 ≤ t ≤ 3, (a) Use the second order Runge-Kutta modified Euler method h Yi+1 · Yi + z [ƒ (ti, Yi) + ƒ (ti+1, Y¡ + hf (ti, Y;))] to approximate the solution to the IVP with h = 1. (b) By approximately what factor would the error in your approximation decrease if instead you were to use the second order RK modified Euler method with h = 0.1? (Do not do the actual numerical calculations as in (a), just use the fact that the truncation error of this method is 0(h²).)

Consider the initial value problem y(1) = 2. y' = 1 + 1 ≤ t ≤ 3, (a) Use the second order Runge-Kutta modified Euler method h Yi+1 · Yi + z [ƒ (ti, Yi) + ƒ (ti+1, Y¡ + hf (ti, Y;))] to approximate the solution to the IVP with h = 1. (b) By approximately what factor would the error in your approximation decrease if instead you were to use the second order RK modified Euler method with h = 0.1? (Do not do the actual numerical calculations as in (a), just use the fact that the truncation error of this method is 0(h²).)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.3: Euler's Method

Problem 1YT: Use Eulers method to approximate the solution of dydtx2y2=1, with y(0)=2, for [0,1]. Use h=0.2.

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