Polynomial Approximation of Differential Equations

Daniele Funaro (Autor)

Buch | Softcover

X, 305 Seiten

2014 | 1. Softcover reprint of the original 1st ed. 1992
Springer Berlin (Verlag)
978-3-662-13878-6 (ISBN)

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This book is devoted to the analysis of approximate solution techniques for differential equations, based on classical orthogonal polynomials. These techniques are popularly known as spectral methods. In the last few decades, there has been a growing interest in this subject. As a matter offact, spectral methods provide a competitive alternative to other standard approximation techniques, for a large variety of problems. Initial ap plications were concerned with the investigation of periodic solutions of boundary value problems using trigonometric polynomials. Subsequently, the analysis was extended to algebraic polynomials. Expansions in orthogonal basis functions were preferred, due to their high accuracy and flexibility in computations. The aim of this book is to present a preliminary mathematical background for be ginners who wish to study and perform numerical experiments, or who wish to improve their skill in order to tackle more specific applications. In addition, it furnishes a com prehensive collection of basic formulas and theorems that are useful for implementations at any level of complexity. We tried to maintain an elementary exposition so that no experience in functional analysis is required.

Special Families of Polynomials.- Orthogonality.- Numerical Integration.- Transforms.- Functional Spaces.- Results in Approximation Theory.- Derivative Matrices.- Eigenvalue Analysis.- Ordinary Differential Equations.- Time-Dependent Problems.- Domain-Decomposition Methods.- Examples.- An Example in Two Dimensions.

Erscheint lt. Verlag	23.8.2014
Reihe/Serie	Lecture Notes in Physics Monographs
Zusatzinfo	X, 305 p. 3 illus.
Verlagsort	Berlin
Sprache	englisch
Maße	170 x 244 mm
Gewicht	554 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	algorithms • Analysis of Convergence • Approximationstheorie • Approximation Theory • Boundary value problem • boundary-value problems • differential equation • eigenvalue • Konvergenzanalyse • Numerical Integration • numerical linear algebra • Numerische Linearalgebra • ordinary differential equation • Randwertaufgaben • Solution • spectral methods • Spektralmethoden
ISBN-10	3-662-13878-6 / 3662138786
ISBN-13	978-3-662-13878-6 / 9783662138786
Zustand	Neuware