Marchuk G.I., Shaidurov V.V. Difference Methods and Their Extrapolations

Springer-Verlag, New York, 1983. – 340 p.
The stimulus for the present work is the growing need for more accurate numerical methods. The rapid advances in computer technology have not provided the resources for computations which make use of methods with low accuracy. The computational speed of computers is continually increasing, while memory still remains a problem when one handles large arrays. More accurate numerical methods allow us to reduce the overall computation time by several orders of magnitude.General Properties.
First-Order Ordinary Differential Equations.
The One-Dimensional Stationary Diffusion Equation.
Elliptic Equations.
Nonstationary Problems.
Extrapolation for Algebraic Problems and Integral Equations.
Appendix.
List of Notation.