论文信息 - Numerical integration by using nonlinear techniques

Numerical integration by using nonlinear techniques

Abstract In this paper several nonlinear techniques, mainly based on the use of Pade approximation and rational interpolation, are given for computing the value of a definite integral. Some convergence properties of these methods are proved. A comparison is made between these non-linear techniques and classical linear techniques on the base of some numerical examples.

Luc Wuytack

[1] P. Henrici. Discrete Variable Methods in Ordinary Differential Equations , 1962 .

[2] R. Piessens,et al. Automatic integration of functions having algebraic end point singularities , 1973 .

[3] David K. Kahaner. Numerical quadrature by the -algorithm , 1972 .

[4] J. N. Lyness,et al. Numerical quadrature and asymptotic expansions , 1967 .

[5] A Genz,et al. Accelerated convergence of sequences of quadrature approximations , 1972 .

[6] Luc Wuytack. On Some Aspects of the Rational Interpolation Problem , 1974 .

[7] L. Fox,et al. Romberg integration for a class of singular integrands , 1967, Comput. J..

[8] W. Gerlach. Nichtlineare Methoden zur Berechnung uneigentlicher Integrale , 1972 .

[9] A generalisation of multistep methods for ordinary differential equations , 1966 .