Improving the Accuracy

As mentioned previously, the FE method derived in Chapter 1 is not the most sophisticated ODE solver. Although it provides sufficient accuracy for most of the applications covered in this book, there are alternative methods available that offer improved accuracy and stability, making them better suited for solving challenging ODE systems. In this chapter, we will focus on enhancing accuracy, and thus we will primarily explore explicit methods. Implicit methods, which exhibit superior stability properties and are better suited for solving stiff ODEs, will be discussed in Chapter 3.