Problem 1: Consider the following Initial Value Problem (IVP)where ? is the dependent variable and ? is the independentvariable: ??=sin(?)?(1??) with ?(0)=?0 and ??0
Note: the analytic solution for this IVP is:?(?)=1+(?_0?1)?^cos(?)?1
Part 1A: Approximate the solution to the IVP using Euler’s methodwith the following conditions: Initial condition ?_0=?1/2; timestep ?=1/16; and time interval ??[0,20]
+ Derive the recursive formula for Euler’s method applied to thisIVP
+ Plot the Euler’s method approximation
+ Plot the absolute error between the approximation and the exactsolution using a semilog plot
Coding errors, please type out.
