This book surveys the most recent research in six key areas related to numerical solutions of differential equations. It covers guaranteed error bounds for ordinary differential equations; an introduction to computational methods for differential equations; numerical solution of differential-algebraic equations, boundary element methods; and perturbation theory for infinite dimensional dynamical systems. It draws together a method that is currently only available in journals, introducing the reader to important current research. This book is written at a level for graduate students and researchers in computational mathematics and in application areas in physics and engineering.

This book surveys the most recent research in six key areas related to numerical solutions of differential equations. It covers guaranteed error bounds for ordinary differential equations; an introduction to computational methods for differential equations; numerical solution of differential-algebraic equations, boundary element methods; and perturbation theory for infinite dimensional dynamical systems. It draws together a method that is currently only available in journals, introducing the reader to important current research. This book is written at a level for graduate students and researchers in computational mathematics and in application areas in physics and engineering.