Practical Time-stepping Schemes

This book is about the numerical solution of the equations for modelling aquifers, heat conduction and diffusion, the dynamic vibration of structures and associated non-linear and coupled problems where the space discretization is done by the finite element method. The results are first or second order ordinary differential equations of a particular form because of their origin. The author discusses the mathematical implications and limitations of the most popular algorithms for their solution. The book includes results of the author's work with engineers and applied scientists over many years which have not previously been assembled and gives an account of other results in the literature. This is a graduate text intended for applied mathematicians and theoretically inclined engineers and scientists. The mathematics is deliberately kept simple but there are many references to sources where further details may be found.