Computational Differential Equations

Many processes in the natural sciences, engineering and finance are described mathematically using ordinary or partial differential equations. Only the simplest or those with special structure can be solved exactly. This subject discusses common techniques for computing numerical solutions to differential equations and introduces the major themes of accuracy, stability and efficiency. Understanding these basic properties of scientific computing algorithms should prevent the unwary from using software packages inappropriately or uncritically, and provide a foundation for devising methods for nonstandard problems. We cover both time-independent problems, in one and higher space dimensions, and evolution equations of hyperbolic or parabolic type.