ABSTRACT
Due to the importance of differential equations in engineering and science, ordinary differential equation (ODE) solution techniques have received a lot of attention in the twentieth century. This chapter discusses numerical techniques to solve an ODE initial value problem (IVP), followed by the application of ODE solution techniques to Process Engineering problems. In addition to determining the step-size, stability analysis has significant practical ramifications on the choice of numerical method for solving ODEs. The "speed" of evolution of the ODE is governed by the smallest eigenvalue, whereas the step-size is limited by the largest eigenvalue. The chapter presents first-, second-, and third-order Runge-Kutta (RK) methods. With different values of weights, RK-2 and RK-3 methods were obtained. The RK methods are popular for solving ODE-IVP because higher-order methods with better accuracy are available; they are relatively easy to code being explicit methods; and they allow adaptive step-sizing.
