Concept explainers
Errors in Euler’s method Consider the following initial value problems.
a. Find the approximations to y(0, 2) and y(0.4) using Euler’s method with time steps of Δt = 0.2, 0.1, 0.05, and 0.025.
b. Using the exact solution given, compute the errors in the Euler approximations at t = 0.2 and t = 0.4.
c. Which time step results in the more accurate approximation? Explain your observations.
d. In general, how does halving the time step affect the error at t = 0.2 and t = 0.4?
29. y’(t) = –y, y(0) = 1; y(t) = e–t
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CALCULUS:EARLY TRANSCENDENTALS-PACKAGE
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