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Problem 1: Consider the following Initial Value Problem (IVP) where ? is the dependent variable and...

Problem 1: Consider the following Initial Value Problem (IVP) where ? is the dependent variable and ? is the independent variable: ?′=sin(?)∗(1−?) with ?(0)=?0 and ? ≥ 0

Note: the analytic solution for this IVP is: y(t) = 1+(y_0 - 0)e^ cos(t)-1

Part 1B: Approximate the solution to the IVP using the Improved Euler’s method with the following conditions: Initial condition ?0=−1/2; time step ℎ=1/16; and time interval ?∈[0,20]
+ Derive the recursive formula for the Improved Euler’s method applied to this IVP
+ Plot the Improved Euler’s method approximation
+ Plot the absolute error between the approximation and the exact solution using a semilog plot

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Colby Messinger answered 2 years ago
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