Publisher description for Numerical solution of partial differential equations : an introduction / K.W. Morton and D.F. Mayers.
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Partial differential equations are the chief means of providing mathematical models in physics, engineering and other fields. Generally these models must be solved numerically. This book provides a concise introduction to standard numerical techniques, ones chosen on the basis of their general utility for practical problems. The authors emphasize finite difference methods for simple examples of parabolic, hyperbolic and elliptic equations; finite element, finite volume and spectral methods are discussed briefly to see how they relate to the main theme. Stability is treated clearly and rigorously using maximum principles, energy methods, and discrete Fourier analysis. Methods are described in detail for simple problems, accompanied by typical graphical results. A key feature is the thorough analysis of the properties of these methods. Plenty of examples and exercises of varying difficulty are supplied.The book will be an excellent choice for students and teachers in mathematics, engineering and computer science departments seeking a concise introduction to the subject.
Library of Congress subject headings for this publication: Differential equations, Partial Numerical solutions