A First Course in the Numerical Analysis of Differential Equations
by Aresh Iserles 1996

This book presents a rigorous account of the fundamentals of numerical analysis
of both ordinary and partial differential equations. The point of departure is
mathematical but the exposition strives to maintain a balance among theoretical,
algorithmic and applied aspects of the subject. In detail, topics covered include
numerical solution of ordinary differential equations by multistep and Runge-Kutta
methods; finite difference and finite elements techniques for the Poisson equation;
a variety of algorithms to solve large, sparse algebraic systems; and methods for
parabolic and hyperbolic differential equations and techniques of their analysis.
The book is accompanied by an appendix that presents brief back-up in a number of
mathematical topics.

Numerical Mathematics by Alfo Quarteroni Ricardo Sacco and Fausto Saleri
2nd Edition 2006

This book provides the mathematical foundations of numerical methods
and demonstrates their performance on examples, exercises and real-life
applications. This is done using the MATLAB software environment, which allows
an easy implementation and testing of the algorithms for any specific class of
problems. The book is addressed to students in Engineering, Mathematics, Physics
and Computer Sciences. In the second edition of this extremely popular textbook
on numerical analysis, the readability of pictures, tables and program headings
has been improved. Several changes in the chapters on iterative methods and on
polynomial approximation have also been made.

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