Methods of Numerical IntegrationAcademic Press, 10 mai 2014 - 626 pages Methods of Numerical Integration, Second Edition describes the theoretical and practical aspects of major methods of numerical integration. Numerical integration is the study of how the numerical value of an integral can be found. This book contains six chapters and begins with a discussion of the basic principles and limitations of numerical integration. The succeeding chapters present the approximate integration rules and formulas over finite and infinite intervals. These topics are followed by a review of error analysis and estimation, as well as the application of functional analysis to numerical integration. A chapter describes the approximate integration in two or more dimensions. The final chapter looks into the goals and processes of automatic integration, with particular attention to the application of Tschebyscheff polynomials. This book will be of great value to theoreticians and computer programmers. |
Table des matières
| 1 | |
| 51 | |
CHAPTER 3 APPROXIMATE INTEGRATION OVER INFINITE INTERVALS | 199 |
CHAPTER 4 ERROR ANALYSIS | 271 |
CHAPTER 5 APPROXIMATE INTEGRATION IN TWO OR MORE DIMENSIONS | 344 |
CHAPTER 6 AUTOMATIC INTEGRATION | 418 |
ON THE PRACTICAL EVALUATION OF INTEGRALS | 463 |
FORTRAN PROGRAMS | 480 |
BIBLIOGRAPHY OF ALGOL FORTRAN AND PLI PROCEDURES | 509 |
BIBLIOGRAPHY OF TABLES | 518 |
BIBLIOGRAPHY OF BOOKS AND ARTICLES | 524 |
| 605 | |
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Expressions et termes fréquents
a₁ abscissas abscissas and weights accuracy adaptive algorithm Anal analytic functions applied approximate integration automatic integration CACM Cauchy principal value Clenshaw-Curtis coefficients Comp convergence cubature cubature formulas defined derivatives differential equations dimensions Doncker dx dy error estimate example fast Fourier transform finite Fourier transform function evaluations Gauss rule Gaussian quadrature Genz given Hence hypercube indefinite integral integrand integration formulas integration rules interpolation interpolatory interval Krylov Laguerre Laplace transform linear Lobatto Lyness Math method multiple integrals Newton-Cotes number of functional number of points Numerical Analysis numerical evaluation numerical integration numerical quadrature obtain orthogonal polynomials oscillatory Phys Piessens quadrature formulas quadrature rules Rabinowitz References Riemann Romberg roundoff Section sequence SIAM Simpson's rule singularity spline subintervals symmetric theorem trapezoidal rule Tschebyscheff Univ variable w₁ weight function x₁ zeros