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Consider the system modeled by the differential equation                               dy/dt - y = t    with initial...

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Advance Math

Consider the system modeled by the differential equation

                              dy/dt - y = t    with initial condition y(0) = 1

the exact solution is given by y(t) = 2et ? t ? 1

 

Note, the differential equation dy/dt - y =t can be written as

                                              dy/dt = t + y

using Euler’s approximation of dy/dt = (y(t + Dt) – y(t))/ Dt

                              (y(t + Dt) – y(t))/ Dt = (t + y)

                               y(t + Dt) = (t + y)Dt + y(t)

                              New Value = change + current value

 

 

  1. Using R implement Euler’s method directly to numerically solve the equation and construct a Table as below – list data to four digits past the decimal point. Submit your R session

               time     ?t = 0.1           ?t = 0.0001        Exact Value       %Relative                  %Relative

                                                                                                             Error ?t = 0.1       Error ?t = 0.0001                    

                  0

                 0.1

                 0.2

                 0.3

                 0.4

                 0.5

                 0.6

                 0.7

                 0.8

                 0.9

                 1.0

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