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Consider the initial value problem with exact solution 2" +26x² + 25x = 50 cos(5t), 1075 104 r(t) = = 35 104 x(0) = 10, I'(0) = 0 -25t sin(5t) (5) (a) Use Heun's method with h = 0.05 to approximate the solution of (4) for t in [0, 10]. Plot the exact solution r(t) and approximate solution on the same graph. What do you observe? Repeat with h = 0.1. What do you observe? (4)

Consider the initial value problem with exact solution 2" +26x² + 25x = 50 cos(5t), 1075 104 r(t) = = 35 104 x(0) = 10, I'(0) = 0 -25t sin(5t) (5) (a) Use Heun's method with h = 0.05 to approximate the solution of (4) for t in [0, 10]. Plot the exact solution r(t) and approximate solution on the same graph. What do you observe? Repeat with h = 0.1. What do you observe? (4)

Calculus For The Life Sciences
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
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 18E: Find the general solution for each differential equation. Verify that each solution satisfies the...
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Consider the initial value problem with exact solution 2" +26x' + 25x = 50 cos(5t), r(t) = = 1075 104 35 104 x(0) = 10, -25t 5 13 I'(0) = 0 (4) sin(5t) (5) (a) Use Heun's method with h = 0.05 to approximate the solution of (4) for t in [0, 10]. Plot the exact solution z(t) and approximate solution on the same graph. What do you observe? Repeat with h = 0.1. What do you observe? (c) Use Backward Euler's Method with h = 0.1 to approximate the solution of (4) for t in [0, 10]. Plot the exact solution z(t) and approximate solution on the same graph. What do you observe? Repeat with h = 0.2. What do you observe?
Transcribed Image Text:Consider the initial value problem with exact solution 2" +26x' + 25x = 50 cos(5t), r(t) = = 1075 104 35 104 x(0) = 10, -25t 5 13 I'(0) = 0 (4) sin(5t) (5) (a) Use Heun's method with h = 0.05 to approximate the solution of (4) for t in [0, 10]. Plot the exact solution z(t) and approximate solution on the same graph. What do you observe? Repeat with h = 0.1. What do you observe? (c) Use Backward Euler's Method with h = 0.1 to approximate the solution of (4) for t in [0, 10]. Plot the exact solution z(t) and approximate solution on the same graph. What do you observe? Repeat with h = 0.2. What do you observe?
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