Numerical Solution of Elliptic and Parabolic Partial Differential Equations
This new book by professor emeritus of mathematics Trangenstein guides mathematicians and engineers on applying numerical methods to physical problems. Numerical ideas are connected to accompanying software, which is also available online. By seeing the complete description of the methods in both theory and implementation, students will more easily gain the knowledge needed to write their own application programs or develop new theory.
The book contains careful development of the mathematical tools needed for analysis of the numerical methods, including elliptic regularity theory and approximation theory. Variational crimes, due to quadrature, coordinate mappings, domain approximation and boundary conditions, are analyzed. The claims are stated with full statement of the assumptions and conclusions, and use subscripted constants that can be traced back to the origination (particularly in the electronic version, which can be found on the accompanying CD-ROM).