Please show your work and justify all answers. 1. Use (forward) Euler's method to approximate the solution of the IVP y'= -3y, y(0) = 1 on the interval [0, 1] with a step size of At = 0.2. You can use a calculator to help with the arithmetic. Compare your approximate value for y(1) with the true value of y(1). 2. Repeat problem 1 with a step size of At = 0.1. Which step size gives better accuracy?
Please show your work and justify all answers. 1. Use (forward) Euler's method to approximate the solution of the IVP y'= -3y, y(0) = 1 on the interval [0, 1] with a step size of At = 0.2. You can use a calculator to help with the arithmetic. Compare your approximate value for y(1) with the true value of y(1). 2. Repeat problem 1 with a step size of At = 0.1. Which step size gives better accuracy?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Please show your work and justify all answers.
1. Use (forward) Euler's method to approximate the solution of the IVP y'= -3y, y(0) = 1
on the interval [0, 1] with a step size of At = 0.2. You can use a calculator to help with
the arithmetic. Compare your approximate value for y(1) with the true value of y(1).
2. Repeat problem 1 with a step size of At = 0.1. Which step size gives better accuracy?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa06fb91f-1445-4bd6-b9dd-268642fc0d22%2Fa9389ed1-b289-41a5-8719-a161b65c2cee%2F5mp992f.jpeg&w=3840&q=75)
Transcribed Image Text:Please show your work and justify all answers.
1. Use (forward) Euler's method to approximate the solution of the IVP y'= -3y, y(0) = 1
on the interval [0, 1] with a step size of At = 0.2. You can use a calculator to help with
the arithmetic. Compare your approximate value for y(1) with the true value of y(1).
2. Repeat problem 1 with a step size of At = 0.1. Which step size gives better accuracy?
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