First Steps in Numerical Analysis
by R. Hosking, S. Joe, D. Joyce, and J. Turner
Number of pages: 338
This book provides an excellent introduction to the elementary concepts and methods of numerical analysis for students meeting the subject for the first time. The subject matter is organized into fundamental topics and presented as a series of steps. At the end of each step, checkpoints are included to allow the reader to gauge their understanding of the concepts introduced.
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by M.N. Spijker - Leiden University
Stability estimates and resolvent conditions in the numerical solution of initial value problems. Contents: Partial differential equations and numerical methods; Linear algebra; Stability in the numerical solution of differential equations; etc.
by Gong Chen, et al. - Wikibooks
We start with finite-precision arithmetic. We then discuss how to solve ordinary differential equations and partial differential equations using the technique of separation of variables. We then introduce numerical time-stepping schemes...
by Todd Young, Martin J. Mohlenkamp - Ohio University
The goals of these notes are to introduce concepts of numerical methods and introduce Matlab in an Engineering framework. The notes were developed by the author in the process of teaching a course on applied numerical methods for Civil Engineering.
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In these notes, we describe the design of a small C++ program which solves numerically the sine-Gordon equation. The program is build progressively to make it multipurpose and easy to modify to solve any system of partial differential equations.