Mathematics - iii (Differential Calculus) - Vol 4

The chapter delves into the fundamental properties that are crucial for the numerical solution of Ordinary Differential Equations (ODEs), focusing on stability and convergence. Stability ensures that errors remain manageable during the numerical method's application, while convergence guarantees that the approximate solution approaches the exact solution as the step size diminishes. Key methods such as Euler’s and Runge-Kutta are highlighted, with an emphasis on their respective stability characteristics and the importance of analyzing the stability region before application.