ABSTRACT
This chapter presents various methods to numerically solve initial-value problems (IVP). Two sources of error are involved in the numerical solution of ordinary differential equations: round-off and truncation. The classical RK4 method is the commonly used technique for numerical solution of first-order (IVP), as it offers the most acceptable balance of accuracy and computational effort. The user-defined function Adams-Bashforth uses the fourth-order Adams-Bashforth formula to estimate the solution of an (IVP). Predictor-corrector methods are a class of techniques that employ a combination of an explicit formula and an implicit formula to solve an (IVP). Mathematical models of most systems in various engineering disciplines comprise one or more first- or higher-order differential equations subject to an appropriate number of initial conditions. There are several MATLAB built-in functions designed for solving a single first-order (IVP) and a system of first-order (IVP). These are known as ODE solvers and include ode23, ode45, and ode113 for non-stiff equations, and ode15s for stiff equations.
