Improved Euler's Method Code

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: ?(?) = 1 + (?0 − 1)?^cos(?)−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

[James Tursa]

What have you done so far? What specific problems are you having with your code?

[Jan]

@Sarita: The forum will not solve homework questions.