Applied Mathematics and Computation 281 (2016) 121–129 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc A novel computational hybrid approach in solving Hankel transform Nagma Irfan ∗ , A.H. Siddiqi Department of Mathematics, School of Basic Sciences and Research, Sharda University, Greater Noida-201306, India a r t i c l e i n f o MSC: 44A15 65R10 Keywords: Hankel transforms Bessel functions Hybrid of Block-pulse functions and Taylor polynomials Noise terms a b s t r a c t In this paper, we use a combination of Taylor and block-pulse functions on the interval [0, 1], that is called Hybrid Functions to estimate fast and stable solution of Hankel trans- form. First hybrid of Block-Pulse and Taylor polynomial basis is obtained and orthonor- malized using Gram–Schmidt process which are used as basis to expand a part of the integrand,r f (r ) appearing in the Hankel transform integral. Thus transforming the integral into a Fourier–Bessel series. Truncating the series, an efficient stable algorithm is obtained for the numerical evaluation of the Hankel transforms of orderν > −1. The novelty of our method is that we give error analysis and stability of the hybrid algorithm and corroborate our theoretical findings by various numerical experiments for the first time. The solutions obtained by projected method indicate that the approach is easy to implement and com- putationally very attractive. © 2016 Elsevier Inc. All rights reserved. 1. Introduction In this paper, we use a combination of Taylor & Block-Pulse functions on the interval [0, 1], that is called hybrid functions, to estimate numerical solution of Hankel Transform. In Recent years, many different basic functions have used to estimate Hankel transform. In our hybrid method we use simple basis, Hybrid of block pulse and Taylor polynomials which are used in solving many engineering problems [1–4]. 1.1. Hankel transform: Definition Several definitions of the Hankel transform appear in the literature. In this paper, we use the definition of the ν th order Hankel transform as defined by Piessens [5] to define the Hankel transform as F ν ( p) ≡ χ ν { f (r )} ≡  ∞ 0 r f (r )J ν ( pr )dr (1) Here, ν may be an arbitrary real or complex number. However, an integral transform needs to be invertible in order to be useful and this restricts the allowable values of ν . If ν is real and ν > − 1/2, and under suitable conditions of integrability of the function, the transform is self-reciprocating and the inversion formula is given by f (r ) = χ −1 ν {F ν ( p)} ≡  ∞ 0 pF ν ( p)J ν ( pr )dp. (2) ∗ Corresponding author: Tel.: +91 9811667135. E-mail address: nagmairfanmath@gmail.com, nagmamath@gmail.com (N. Irfan). http://dx.doi.org/10.1016/j.amc.2016.01.028 0096-3003/© 2016 Elsevier Inc. All rights reserved.