Write Matlab code to find a), b) and d).
Consider the following IVP:
y' = -20y + 20 cost - sint, 0 ? t ? 2, y(0) = 0;
The exact solution of this IVP is:
y = -e$^{-20t}$ + cos t.
With N = 5, h = 0.4, and t$_i$ = 0.4i, for i = 0, 1, 2, 3, 4, 5.
a) Find approximate solutions using the Euler's Method and compare these
results with exact solutions.
b) Calculate the error bound for (1.2) using Euler's method and compare the
actual error.
c) Find approximate solutions using the Modified Euler's Method (Runge-
Kutta method of order two) and compare these results with exact solutions.
d) Find approximate solutions using the Runge-Kutta method of order four
and compare these results with exact solutions..