Discretization of Continuous Systems

Abstract

In this chapter, the discretization of continuous systems is presented. The explicit and implicit discrete maps are discussed for numerical predictions of continuous systems. Basic discrete schemes are presented which include forward and backward Euler methods, midpoint, and trapezoidal rule method. An introduction to Runge–Kutta methods is presented, and the Taylor series method and second-order Runge–Kutta method are introduced. The explicit Runge–Kutta methods for third and fourth order are systematically presented. The implicit Runge–Kutta methods are discussed based on the polynomial interpolation, which include a generalized implicit Runge–Kutta method, Gauss method, Radau method, and Lotta methods. In addition to one-step methods, implicit and explicit multi-step methods are discussed, including Adams–Bashforth method, Adams–Moulton methods, and explicit and implicit Adams methods.