Problem 1 – Numerical Solution of First-Order ODE:
Consider the following ODE:
dy/dt = -2/3 y
which has the initial condition y(t = 0) = 3.
a) Use the Runge-Kutta method to solve the ODE for h = 0.1 by hand – show the first two steps including the computation of ki, i = 1, 2, 3, 4.
b) Now, write a program for the Runge-Kutta method and use this program to numerically solve the ODE for h = 0.1 from t = 0 to t = 2. Present all intermediate steps in your solution, i.e. y0, y*1, y*2, y*3 etc.