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Book Description
The subject of partial differential equations holds an exciting place in mathematics. Inevitably， the subject falls into several areas of mathematics. At one extreme the interest lies in the existence and uniqueness of solutions， and the functional analysis of the proofs of these properties. At the other extreme lies the applied mathematical and engineering quest to find useful solutions， either analytically or numerically， to these important equations which can be used in design and construction. The book presents a clear introduction of the methods and underlying theory used in the numerical solution of partial differential equations. Throughout， the emphasis is on the practical solution rather than the theoretical background， without sacrificing rigour. After revising the mathematical preliminaries， the book covers the finite difference method of parabolic or heat equations， hyperbolic or wave equations and elliptic or Laplace equations. Numerical Methods for Partial Differential Equations provides a complete introduction to the subject， suitable for second or third year undergraduates or for non-specialist graduate courses. Many illustrative exercises are provided， most with full solutions or advice on creating appropriate computer algorithms.