An Introduction to Fast Fourier Transform Methods for Partial Differential Equations, With Applications (Electronic and Electrical Engineering Resear) - Hardcover

Pickering, Morgan

9780471912613: An Introduction to Fast Fourier Transform Methods for Partial Differential Equations, With Applications (Electronic and Electrical Engineering Resear)

Hardcover

ISBN 10: 0471912611 ISBN 13: 9780471912613

Publisher: Research Studies Pr Ltd, 1986

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Fast Fourier transform (FFT) methods are well established for solving certain types of partial differential equations (PDE). This book is written at an introductory level with the non-specialist user in mind. It first deals with basic ideas and algorithms which may be used to solve problems using simple geometries--the fast Fourier transform is employed and thorough details of the computations are given for a number of illustrative problems. The text proceeds to problems with irregular boundaries, using the capacity matrix approach, and also to more advanced PDE, for which fast solvers may be used as the basis for iterative methods. The use of a numerical Laplace transform technique for certain time-dependent problems is also covered. Throughout the book, the approach is designed to illustrate the essential ideas of the methods employed. References are given for further reading of more advanced or specialized topics.

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Synopsis

Fast Fourier Transform (FFT) methods are well established as efficient methods for solving certain types of partial differential equation; this book is written at an introductory level with the non-specialist user particularly in mind. The first part of the book deals with some of the basic ideas and algorithms which may be used to solve suitable problems with simple geometries, using the fast Fourier transform, and computational details are given for a number of illustrative examples. These techniques are applied in later chapters to problems with irregularly shaped boundaries using the capacity matrix approach and also to more complicated partial differential equations, for which fast-solvers may be used as the basis of an iterative method of solution. The use of a numerical Laplace transform technique for certain time-dependent problems is also discussed. Thoughout the book the approach used is designed to illustrate the essential ideas of the methods, and references are given for further reading of more advanced or specialised topics.

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