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Problem of the Week: Consider Euler's method, applied to the differential equation = y, with initial condition y(0) = 1. Suppose the step size is h = ! for some natural number %3D п. 1. Show that for all i, y¡ = (1+ )yi-1- 2. Explain why this means that our approximation for y(1) is (1 +)". 3. The exact solution to this differential equation is y = eª. Explain how this exercise relates to the fact that 1 e = lim (1 + = n

Problem of the Week: Consider Euler's method, applied to the differential equation = y, with initial condition y(0) = 1. Suppose the step size is h = ! for some natural number %3D п. 1. Show that for all i, y¡ = (1+ )yi-1- 2. Explain why this means that our approximation for y(1) is (1 +)". 3. The exact solution to this differential equation is y = eª. Explain how this exercise relates to the fact that 1 e = lim (1 + = n

Advanced Engineering Mathematics
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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Problem of the Week: Consider Euler's method, applied to the differential equation = y, with initial condition y(0) = 1. Suppose the step size is h = for some natural number n n. 1. Show that for all i, yi (1+ )i-1- 2. Explain why this means that our approximation for y(1) is (1+ )". 3. The exact solution to this differential equation is y = e". Explain how this exercise relates to the fact that e = lim (1+=)".
Transcribed Image Text:Problem of the Week: Consider Euler's method, applied to the differential equation = y, with initial condition y(0) = 1. Suppose the step size is h = for some natural number n n. 1. Show that for all i, yi (1+ )i-1- 2. Explain why this means that our approximation for y(1) is (1+ )". 3. The exact solution to this differential equation is y = e". Explain how this exercise relates to the fact that e = lim (1+=)".
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