Numerical Differential Equations ─ Theory and Technique, ODE Methods, Finite Differences, Finite Elements and Collocation

The book presents numerical differential equations to graduate (doctoral) students. It includes the three standard approaches to numerical PDE, FDM, FEM and CM, and the two most common time stepping techniques, FDM and Runge-Kutta. We present both the numerical technique and the supporting mathematical theory.The applied techniques include those that arise in the present literature. The supporting mathematical theory includes the general convergence theory. This material is easily accessible to students with basic knowledge of mathematical analysis, Lebesgue measure and the basics of Hilbert spaces and Banach spaces. Nevertheless, we have made the book free standing in most respects. Most importantly, the terminology is developed within the text.The material is developed in the context of several interesting application areas such as finance, aerospace, mathematical biology, fluid mechanics.