In Problems 14–24, you will need a computer and a programmed version of the vectorized classical fourth-order Runge–Kutta algorithm. (At the instructor’s discretion, other algorithms may be used.)†
Using the vectorized Runge–Kutta algorithm for systems with , approximate the solution to the initial value problem at .
Compare this approximation to the actual solution.
The solution is and .
Write the equation as and
The transformation of the equation is:
The initial conditions are:
For the solution, apply the Runge-Kutta method in MATLAB, and the solution is and .
By putting the value of
Therefore, the approximation solution is and .
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