scholarly journals Stable Numerical Evaluation of Finite Hankel Transforms and Their Application

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Manoj P. Tripathi ◽  
B. P. Singh ◽  
Om P. Singh
Keyword(s):  
Stability Analysis ◽  
Heat Equation ◽  
Numerical Experiments ◽  
Numerical Evaluation ◽  
Radiation Condition ◽  
Hankel Transform ◽  
Basis Functions ◽  
Infinite Cylinder ◽  
Stable Algorithm ◽  
Hankel Transforms

A new stable algorithm, based on hat functions for numerical evaluation of Hankel transform of order ν>-1, is proposed in this paper. The hat basis functions are used as a basis to expand a part of the integrand, rf(r), appearing in the Hankel transform integral. This leads to a very simple, efficient, and stable algorithm for the numerical evaluation of Hankel transform. The novelty of our paper is that we give error and stability analysis of the algorithm and corroborate our theoretical findings by various numerical experiments. Finally, an application of the proposed algorithm is given for solving the heat equation in an infinite cylinder with a radiation condition.

A stable algorithm for numerical evaluation of Hankel transforms using Haar wavelets

2009 ◽  
Vol 53 (4) ◽  
pp. 451-466 ◽  
Author(s):  
Rajesh K. Pandey ◽  
Om Prakash Singh ◽  
Vineet K. Singh
Keyword(s):  
Numerical Evaluation ◽  
Haar Wavelets ◽  
Stable Algorithm ◽  
Hankel Transforms

scholarly journals Optimal solution of the fractional order breast cancer competition model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
H. Hassani ◽  
J. A. Tenreiro Machado ◽  
Z. Avazzadeh ◽  
E. Safari ◽  
S. Mehrabi
Keyword(s):  
Breast Cancer ◽  
Fractional Order ◽  
Legendre Polynomials ◽  
Numerical Experiments ◽  
Optimal Solution ◽  
Optimization Method ◽  
Competition Model ◽  
Basis Functions ◽  
Cell Populations ◽  
Operational Matrices

AbstractIn this article, a fractional order breast cancer competition model (F-BCCM) under the Caputo fractional derivative is analyzed. A new set of basis functions, namely the generalized shifted Legendre polynomials, is proposed to deal with the solutions of F-BCCM. The F-BCCM describes the dynamics involving a variety of cancer factors, such as the stem, tumor and healthy cells, as well as the effects of excess estrogen and the body’s natural immune response on the cell populations. After combining the operational matrices with the Lagrange multipliers technique we obtain an optimization method for solving the F-BCCM whose convergence is investigated. Several examples show that a few number of basis functions lead to the satisfactory results. In fact, numerical experiments not only confirm the accuracy but also the practicability and computational efficiency of the devised technique.

Two stable methods with numerical experiments for solving the backward heat equation

2011 ◽  
Vol 61 (2) ◽  
pp. 266-284 ◽  
Author(s):  
Fabien Ternat ◽  
Oscar Orellana ◽  
Prabir Daripa
Keyword(s):  
Heat Equation ◽  
Numerical Experiments

scholarly journals A Relation between Laplace and Hankel Transforms

1962 ◽  
Vol 5 (3) ◽  
pp. 114-115 ◽  
Author(s):  
B. R. Bhonsle
Keyword(s):  
Laplace Transform ◽  
Hankel Transform ◽  
Laplace And Hankel Transforms ◽  
Hankel Transforms ◽  
The Laplace Transform ◽  
Image Position

The Laplace transform of a function f(t) ∈ L(0, ∞) is defined by the equationand its Hankel transform of order v is defined by the equationThe object of this note is to obtain a relation between the Laplace transform of tμf(t) and the Hankel transform of f(t), when ℛ(μ) > − 1. The result is stated in the form of a theorem which is then illustrated by an example.

scholarly journals Stability analysis of a system coupled to a heat equation

Automatica ◽  
2019 ◽  
Vol 99 ◽  
pp. 195-202 ◽  
Author(s):  
Lucie Baudouin ◽  
Alexandre Seuret ◽  
Frédéric Gouaisbaut
Keyword(s):  
Stability Analysis ◽  
Heat Equation

Numerical integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering

Geophysics ◽  
1979 ◽  
Vol 44 (7) ◽  
pp. 1287-1305 ◽  
Author(s):  
Walter L. Anderson
Keyword(s):  
Large Range ◽  
Digital Filtering ◽  
Hankel Transform ◽  
Kernel Functions ◽  
General Nature ◽  
Earth Model ◽  
Hankel Transforms ◽  
Quadrature Methods ◽  
Test Driver ◽  
Different Order

A linear digital filtering algorithm is presented for rapid and accurate numerical evaluation of Hankel transform integrals of orders 0 and 1 containing related complex kernel functions. The kernel for Hankel transforms is defined as the non‐Bessel function factor of the integrand. Related transforms are defined as transforms, of either order 0 or 1, whose kernel functions are related to one another by simple algebraic relationships. Previously saved kernel evaluations are used in the algorithm to obtain rapidly either order transform following an initial convolution operation. Each order filter is designed with identical abscissas over a large range so that an adaptive convolution procedure can be applied to a large class of kernels. Different order Hankel transforms with related kernels are often found in electromagnetic (EM) applications. Because of the general nature of this algorithm, the need to design new filters should not be necessary for most applications. Accuracy of the filters is comparable to that of single‐precision numerical quadrature methods, provided well‐behaved kernels and moderate values of the transform argument are used. Filtering errors of less than 0.005 percent are demonstrated numerically using known analytical Hankel transform pairs. The digital filter accuracy is also illustrated by comparison with other published filters for computing the apparent resistivity for a Schlumberger array over a horizontally layered earth model. The algorithm is written in Fortran IV and is listed in the Appendix along with a test driver program. Detailed comments are included to define sufficiently all calling parameter requirements.

scholarly journals A heat equation for freezing processes with phase change: stability analysis and applications

2015 ◽  
Vol 89 (4) ◽  
pp. 833-849 ◽  
Author(s):  
C. J. Backi ◽  
J. D. Bendtsen ◽  
J. Leth ◽  
J. T. Gravdahl
Keyword(s):  
Stability Analysis ◽  
Heat Equation ◽  
Phase Change

Computation of Green’s tensor integrals for three‐dimensional electromagnetic problems using fast Hankel transforms

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1754-1759 ◽  
Author(s):  
Walter L. Anderson
Keyword(s):  
Half Space ◽  
Three Dimensional ◽  
Hankel Transform ◽  
Electromagnetic Modeling ◽  
Electromagnetic Problems ◽  
Hankel Transforms ◽  
Homogeneous Half Space ◽  
Green's Tensor ◽  
Green’S Tensor ◽  
The Many

A new method is presented that rapidly evaluates the many Green’s tensor integrals encountered in three‐dimensional electromagnetic modeling using an integral equation. Application of a fast Hankel transform (FHT) algorithm (Anderson, 1982) is the basis for the new solution, where efficient and accurate computation of Hankel transforms are obtained by related and lagged convolutions (linear digital filtering). The FHT algorithm is briefly reviewed and compared to earlier convolution algorithms written by the author. The homogeneous and layered half‐space cases for the Green’s tensor integrals are presented in a form so that the FHT can be easily applied in practice. Computer timing runs comparing the FHT to conventional direct convolution methods are discussed, where the FHT’s performance was about 6 times faster for a homogeneous half‐space, and about 108 times faster for a five‐layer half‐space. Subsequent interpolation after the FHT is called is required to compute specific values of the tensor integrals at selected transform arguments; however, due to the relatively small lagged convolution interval used (same as the digital filter’s), a simple and fast interpolation is sufficient (e.g., by cubic splines).

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