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| :: Purpose and Summary |
Equal emphasis on theory and numerical algorithms
Our book provides an elementary yet comprehensive introduction to the
numerical solution of partial differential equations (PDEs). Used to
model important phenomena, such as the heating of apartments and the
behavior of electromagnetic waves, these equations have applications
in engineering and the life sciences, and most can only be solved
approximately using computers. We provide detailed descriptions of the
four major classes of discretization methods for PDEs (finite
difference method, finite volume method, spectral method, and finite
element method) and runnable MATLAB code for each of the
discretization methods and exercises. We also give self-contained
convergence proofs for each method using the tools and techniques
required for the general convergence analysis but adapted to the
simplest setting to keep the presentation clear and complete. This
book is intended for advanced undergraduate and early graduate
students in numerical analysis and scientific computing and
researchers in related fields. It is appropriate for a course on
numerical methods for partial differential equations.
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