Texts: solve part 6 and 7
6. Write out the recursive equation for an Euler-Cauchy scheme and
repeat the previous three steps using the Euler-Cauchy method.
7. Compare the estimated values to the correct values from the analytical solution at the points tn for both of the two versions of the numerical scheme and for both step sizes. Explain how you have made this comparison and what your results mean.
Differential Equation
The ordinary differential equation for this assignment is given here:
dx/dt = -Ax - A2e^-t
It has an analytical solution
x(t) = Ae^-At + A2e^-t
where
A = 0.15 and A2 = 0.25, A = 4.0, and o = 2.5.
It is to be solved from t = 0 to t = 30.0, with a step size h = 0.1, for the parameter values and initial condition given here:
A = 0.15, A2 = 0.25, A = 4.0, and o = 2.5.
