a) For a fixed delta t(i+1)= delta t, the linear equation, x = Ax, x(t0)=x0 has the solution... Show that the Runge Kutta method (below) is 3rd order and not 4th order for the above linear equation.
bi) Find the exact solution of x = -2x, x0 = 3
bii) Find the numerical solution for two simulation steps using explicit Euler and delta t=0.2.
biii) Find the numerical solution for two simulation steps using modified Euler and delta t=0.2.
biv) Find the global error at t=0.4 for the above methods. What do you expect will happen to these errors if the step size is halved?
This solution is provided in 718 words combined and attached in two separate .doc files. It uses step-by-step equations for solving the mathematical problems.