Euler’s method and beyond
1.1 Ordinary differential equations and the Lipschitz condition
We commence our exposition of the computational aspects of differential equations by examining closely numerical methods for ordinary differential equations (ODEs). This is important because of the central role of ODEs in a multitude of applications. Not less crucial is the critical part that numerical ODEs play in the design and analysis of computational methods for partial differential equations (PDEs). Thus, even if your main interest is in solving PDEs, ...