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Solve the differential equation t dy dt 1 y(0)=1 by the Euler method with h=0.1 to get y(0.2). Then repeat with h=0.2 to get another estimate of y(0.2). Extrapolate these results assuming that errors are proportional to step-size, and compare the derived result to the analytical result.

Solve the differential equation t dy dt 1 y(0)=1 by the Euler method with h=0.1 to get y(0.2). Then repeat with h=0.2 to get another estimate of y(0.2). Extrapolate these results assuming that errors are proportional to step-size, and compare the derived result to the analytical result.

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
Section11.3: Euler's Method
Problem 22E
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4. Solve the differential equation dy y(0)=1 y' by the Euler method with h=0.1 to get y(0.2). Then repeat with h=0.2 to get another estimate of y(0.2). Extrapolate these results assuming that errors are proportional to step-size, and compare the derived result to the analytical result. dt
Transcribed Image Text:4. Solve the differential equation dy y(0)=1 y' by the Euler method with h=0.1 to get y(0.2). Then repeat with h=0.2 to get another estimate of y(0.2). Extrapolate these results assuming that errors are proportional to step-size, and compare the derived result to the analytical result. dt
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