Nagma Irfan - Academia.edu (original) (raw)

Papers by Nagma Irfan

Research paper thumbnail of An Application of Wavelet Technique in Numerical Evaluation of Hankel Transforms

International Journal of Nonlinear Sciences and Numerical Simulation, 2015

This paper endeavors to formulate a stable and fast algorithm for the first time that is quite ac... more This paper endeavors to formulate a stable and fast algorithm for the first time that is quite accurate and fast for numerical evaluation of the Hankel transform using wavelets which are usually difficult to solve analytically so it is required to obtain the approximate solution. So we have proposed an approach depending on separating the integrand rf(r)Jnu(pr)rf(r){J_\nu}(pr)rf(r)Jnu(pr) into two components, the slowly varying components rf(r)rf(r)rf(r) and the rapidly oscillating component Jnu(pr){J_\nu}(pr)Jnu(pr). Then either rf(r)rf(r)rf(r) is expanded into wavelet series using wavelets orthonormal basis which are first derived and truncating the series at an optimal level or approximating rf(r)rf(r)rf(r) by a quadratic over the subinterval using the Filon quadrature philosophy. A good covenant between the obtained solution and some well-known results has been obtained. The solutions obtained by proposed wavelet method indicate that the approach is easy to implement and computationally very attractive. The novelty of our method is tha...

Research paper thumbnail of A novel computational hybrid approach in solving Hankel transform

Applied Mathematics and Computation, 2016

In this paper, we use a combination of Taylor and block-pulse functions on the interval [0, 1], t... more 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 transform. First hybrid of Block-Pulse and Taylor polynomial basis is obtained and orthonormalized 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 order ν > −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 computationally very attractive.

Research paper thumbnail of Application of Wavelets in Numerical Evaluation of Hankel Transform Arising in Seismology

Industrial and Applied Mathematics, 2015

The computation of electromagnetic (EM) fields for 1-D layered earth model requires evaluation of... more The computation of electromagnetic (EM) fields for 1-D layered earth model requires evaluation of Hankel transform. In this paper we propose a stable algorithm for the first time that is quite accurate and fast for numerical evaluation of the Hankel transform using wavelets arising in seismology. We have projected an approach depending on separating the integrand tf(t)J ν (pt) into two components; the slowly varying components tf(t) and the rapidly oscillating component J ν (pt). Then either tf(t) is expanded into wavelet series using wavelets orthonormal basis and truncating the series at an optimal level or approximating tf(t) by a quadratic over the subinterval using the Filon quadrature philosophy. The solutions obtained by proposed wavelet method applied on three test functions indicate that the approach is easy to implement and computationally very attractive. We have supported a new efficient and stable technique based on compactly supported orthonormal wavelet bases.

Research paper thumbnail of Sine-Cosine Wavelets Approach in Numerical Evaluation of Hankel Transform for Seismology

Applied Mathematical Modelling, 2016

The computation of electromagnetic (EM) fields for 1-Dlayered earth model requires evaluation of ... more The computation of electromagnetic (EM) fields for 1-Dlayered earth model requires evaluation of Hankel transform. In this paper we propose a stable algorithm for the first time that is quite accurate and fast for numerical evaluation of the Hankel transform using Sine-Cosine wavelets arising in seismology. We have projected an approach depending on separating the integrand rf (r) J ν (pr) into two components; the slowly varying components rf (r) and the rapidly oscillating component J ν (pr). Then either rf (r) is expanded into wavelet series using Sine-Cosine wavelets orthonormal basis and truncating the series at an optimal level or approximating rf (r) by a quadratic over the subinterval using the Filon quadrature philosophy. The solutions obtained by proposed Sine-Cosine wavelet method applied on 5 test functions indicate that the approach is easy to implement and computationally very attractive. We have supported a new efficient and stable technique based on compactly supported orthonormal wavelet bases.

Research paper thumbnail of A Wavelet Algorithm for Fourier-Bessel Transform Arising in Optics

International Journal of Engineering Mathematics, 2015

The aim of the paper is to propose an efficient and stable algorithm that is quite accurate and f... more The aim of the paper is to propose an efficient and stable algorithm that is quite accurate and fast for numerical evaluation of the Fourier-Bessel transform of order ν, ν>-1, using wavelets. The philosophy behind the proposed algorithm is to replace the part tf(t) of the integral by its wavelet decomposition obtained by using CAS wavelets thus representing Fν(p) as a Fourier-Bessel series with coefficients depending strongly on the input function tf(t). The wavelet method indicates that the approach is easy to implement and thus computationally very attractive.

Research paper thumbnail of CV (1)

Research paper thumbnail of An Application of Wavelet Technique in Numerical Evaluation of Hankel Transforms

International Journal of Nonlinear Sciences and Numerical Simulation, 2015

This paper endeavors to formulate a stable and fast algorithm for the first time that is quite ac... more This paper endeavors to formulate a stable and fast algorithm for the first time that is quite accurate and fast for numerical evaluation of the Hankel transform using wavelets which are usually difficult to solve analytically so it is required to obtain the approximate solution. So we have proposed an approach depending on separating the integrand rf(r)Jnu(pr)rf(r){J_\nu}(pr)rf(r)Jnu(pr) into two components, the slowly varying components rf(r)rf(r)rf(r) and the rapidly oscillating component Jnu(pr){J_\nu}(pr)Jnu(pr). Then either rf(r)rf(r)rf(r) is expanded into wavelet series using wavelets orthonormal basis which are first derived and truncating the series at an optimal level or approximating rf(r)rf(r)rf(r) by a quadratic over the subinterval using the Filon quadrature philosophy. A good covenant between the obtained solution and some well-known results has been obtained. The solutions obtained by proposed wavelet method indicate that the approach is easy to implement and computationally very attractive. The novelty of our method is tha...

Research paper thumbnail of A novel computational hybrid approach in solving Hankel transform

Applied Mathematics and Computation, 2016

In this paper, we use a combination of Taylor and block-pulse functions on the interval [0, 1], t... more 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 transform. First hybrid of Block-Pulse and Taylor polynomial basis is obtained and orthonormalized 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 order ν > −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 computationally very attractive.

Research paper thumbnail of Application of Wavelets in Numerical Evaluation of Hankel Transform Arising in Seismology

Industrial and Applied Mathematics, 2015

The computation of electromagnetic (EM) fields for 1-D layered earth model requires evaluation of... more The computation of electromagnetic (EM) fields for 1-D layered earth model requires evaluation of Hankel transform. In this paper we propose a stable algorithm for the first time that is quite accurate and fast for numerical evaluation of the Hankel transform using wavelets arising in seismology. We have projected an approach depending on separating the integrand tf(t)J ν (pt) into two components; the slowly varying components tf(t) and the rapidly oscillating component J ν (pt). Then either tf(t) is expanded into wavelet series using wavelets orthonormal basis and truncating the series at an optimal level or approximating tf(t) by a quadratic over the subinterval using the Filon quadrature philosophy. The solutions obtained by proposed wavelet method applied on three test functions indicate that the approach is easy to implement and computationally very attractive. We have supported a new efficient and stable technique based on compactly supported orthonormal wavelet bases.

Research paper thumbnail of Sine-Cosine Wavelets Approach in Numerical Evaluation of Hankel Transform for Seismology

Applied Mathematical Modelling, 2016

The computation of electromagnetic (EM) fields for 1-Dlayered earth model requires evaluation of ... more The computation of electromagnetic (EM) fields for 1-Dlayered earth model requires evaluation of Hankel transform. In this paper we propose a stable algorithm for the first time that is quite accurate and fast for numerical evaluation of the Hankel transform using Sine-Cosine wavelets arising in seismology. We have projected an approach depending on separating the integrand rf (r) J ν (pr) into two components; the slowly varying components rf (r) and the rapidly oscillating component J ν (pr). Then either rf (r) is expanded into wavelet series using Sine-Cosine wavelets orthonormal basis and truncating the series at an optimal level or approximating rf (r) by a quadratic over the subinterval using the Filon quadrature philosophy. The solutions obtained by proposed Sine-Cosine wavelet method applied on 5 test functions indicate that the approach is easy to implement and computationally very attractive. We have supported a new efficient and stable technique based on compactly supported orthonormal wavelet bases.

Research paper thumbnail of A Wavelet Algorithm for Fourier-Bessel Transform Arising in Optics

International Journal of Engineering Mathematics, 2015

The aim of the paper is to propose an efficient and stable algorithm that is quite accurate and f... more The aim of the paper is to propose an efficient and stable algorithm that is quite accurate and fast for numerical evaluation of the Fourier-Bessel transform of order ν, ν>-1, using wavelets. The philosophy behind the proposed algorithm is to replace the part tf(t) of the integral by its wavelet decomposition obtained by using CAS wavelets thus representing Fν(p) as a Fourier-Bessel series with coefficients depending strongly on the input function tf(t). The wavelet method indicates that the approach is easy to implement and thus computationally very attractive.

Research paper thumbnail of CV (1)