Question: Consider the following Initial Value Problem (IVP) where () is the dependent function: = 2 + 1.14 cos(^/2 ) with (0) = sub0 and 0

Consider the following Initial Value Problem (IVP) where () is the dependent function:

= 2 + 1.14 cos(^/2 ) with (0) = sub0 and 0

Approximate the solution to the IVP using the Improved Euler's method with the following conditions:

Initial condition 0 = 1, time steps = 1/8 , 1/16 , 1/32 , 1/64 , and time interval [0,20]

+ Plot the Improved Euler's method approximation for all 4 time steps

+ Discuss the results of these approximations

Approximate the solution to the IVP using the RK4 method with the following conditions:

Initial condition sub0 = 1; time steps = 1/8 , 1/16 , 1/32 , 1/64 ; and time interval [0,20]

+ Plot the RK4 approximation for all 4 time steps

+ Discuss the results of these approximations

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