Analysis of Discretization Methods for Ordinary Differential Equations

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The book delves into the significance of differential equations in science and engineering, highlighting the numerical analysts’ role in generating solutions through "finitization." It emphasizes the transformation of differential equations into difference equations, particularly on grid points, and the evolution of finite difference methods with the advent of electronic computers. The text also discusses the extensive research and innovations in finite-difference methods for solving first-order ordinary differential equations, noting that many recent developments are variations on established techniques.