Question

In: Advanced Math

Consider the system modeled by the differential equation dy/dt - y = t with initial condition y(0) = 1

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

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

Expert Solution

Colby Messinger answered 2 years ago

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