Runge-Kutta method

a. Assumes that acceleration varies linearly between \(t_{i}\) and \(t_{i}+\theta \Delta t ; \theta \geq 1\)

b. Assumes that acceleration varies linearly between \(t_{i}\) and \(t_{i+1}\); can lead to negative damping

c. Based on the solution of equivalent system of first-order equations

d. Same as Wilson method with \(\theta=1\)

e. Uses finite difference expressions for \(\dot{x}_{i+1}\) and \(\ddot{x}_{i+1}\) in terms of \(x_{i-2}, x_{i-1}, x_{i}\), and \(x_{i+1}\)

f. Conditionally stable