Indefinite integration of oscillatory functions by the Chebyshev series expansion

A Numerical Integration Method by Using Generalized Series of Functions

On the convergence of the method for indefinite integration of oscillatory and singular functions

We consider the problem of convergence and error estimation of the method for computing indefinite integrals proposed in [P. Keller, A method for indefinite integration of oscillatory and singular functions, Numerical Algorithms 46(3) (2007), 219–251]. To this end, we have analysed the properties of the difference operator related to the difference equation for the Chebyshev coefficients of a f...

Chebyshev Series Expansion of Inverse Polynomials

if the polynomial has no roots in [−1, 1]. If the inverse polynomial is decomposed into partial fractions, the an are linear combinations of simple functions of the polynomial roots. If the first k of the coefficients an are known, the others become linear combinations of these with expansion coefficients derived recursively from the bj ’s. On a closely related theme, finding a polynomial with ...

a numerical integration method by using generalized series of functions

Series expansion of Wiener integrals via block pulse functions

In this paper, a suitable numerical method based on block pulse functions is introduced to approximate the Wiener integrals which the exact solution of them is not exist or it may be so hard to find their exact solutions. Furthermore, the error analysis of this method is given. Some numerical examples are provided which show that the approximation method has a good degree of accuracy. The main ...