Part 2 : Runge Kutta Method : Use the Runge-Kutta method of order 4 with h=0.1 to approximate the solution of IVP y^(')=y-(y)/(t),1

Question

Part 2 : Runge Kutta Method : Use the Runge-Kutta method of order 4 with

h=0.1

to approximate the solution of IVP

y^(')=y-(y)/(t),1<=t<=2,y(1)=(1)/(2).

Use the data points generated by the Runge-Kutta method to find the best function that fits this data in the least squares sense. Use the resulting function to approximate the following values of

y

: (a)

y(1.02)

, (b)

y(1.67)

(c)

y(1.98)

. Compare with the values of the exact solution

y=(e^(t-1))/(2t)

.

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