scholarly journals On the numerical computation of cylindrical conductor internal impedance for complex arguments of large magnitude

2017 ◽  
Vol 30 (1) ◽  
pp. 81-91 ◽  
Author(s):  
Slavko Vujevic ◽  
Dino Lovric
Keyword(s):  
Numerical Computation ◽  
Numerical Algorithm ◽  
Bessel Functions ◽  
Unit Length ◽  
Exact Formula ◽  
Asymptotic Approximations ◽  
Modified Bessel Functions ◽  
Large Magnitude ◽  
Internal Impedance ◽  
Cylindrical Conductors

In this paper a numerical algorithm for computation of per-unit-length internal impedance of cylindrical conductors under complex arguments of large magnitude is presented. The presented algorithm either numerically solves the scaled exact formula for internal impedance or employs asymptotic approximations of modified Bessel functions when applicable. The formulas presented can be used for computation of per-unit-length internal impedance of solid cylindrical conductors as well as tubular cylindrical conductors.

scholarly journals Computation of per-unit-length internal impedance of a multilayer cylindrical conductor with possible dielectric layers

2020 ◽  
Vol 33 (4) ◽  
pp. 605-616
Author(s):  
Dino Lovric ◽  
Slavko Vujevic ◽  
Ivan Krolo
Keyword(s):  
Magnetic Field ◽  
Maxwell Equations ◽  
Bessel Functions ◽  
Unit Length ◽  
Dielectric Layers ◽  
Electric And Magnetic Fields ◽  
Electric And Magnetic Field ◽  
Internal Impedance ◽  
Novel Method ◽  
Displacement Currents

In this manuscript, a novel method for computation of per-unit-length internal impedance of a cylindrical multilayer conductor with conductive and dielectric layers is presented in detail. In addition to this, formulas for computation of electric and magnetic field distribution throughout the entire multilayer conductor (including dielectric layers) have been derived. The presented formulas for electric and magnetic field in conductive layers have been directly derived from Maxwell equations using modified Bessel functions. However, electric and magnetic field in dielectric layers has been computed indirectly from the electric and magnetic fields in contiguous conductive layers which reduces the total number of unknowns in the system of equations. Displacement currents have been disregarded in both conductive and dielectric layers. This is justifiable if the conductive layers are good conductors. The validity of introducing these approximations is tested in the paper versus a model that takes into account displacement currents in all types of layers.

UNIFORM ASYMPTOTIC APPROXIMATIONS FOR THE WHITTAKER FUNCTIONS Mκ,iμ(z) AND Wκ,iμ(z)

2003 ◽  
Vol 01 (02) ◽  
pp. 199-212 ◽  
Author(s):  
T. M. DUNSTER
Keyword(s):  
Hypergeometric Functions ◽  
Turning Point ◽  
Bessel Functions ◽  
Asymptotic Approximations ◽  
Whittaker Functions ◽  
Modified Bessel Functions ◽  
Airy Functions ◽  
Double Pole ◽  
Confluent Hypergeometric Functions ◽  
Uniform Reduction

Uniform asymptotic approximations are obtained for the Whittaker's confluent hypergeometric functions Mκ, iμ(z) and Wκ, iμ(z), where κ, μ and z are real. Three cases are considered, and when taken together, result in approximations which are valid for κ → ∞ uniformly for 0 ≤ μ < ∞, 0 < z < ∞, and also for μ → ∞ uniformly for 0 ≤ κ < ∞, 0 < z < ∞. The results are obtained by an application of general asymptotic theories for differential equations either having a coalescing turning point and double pole with complex exponent, or a fixed simple turning point. The resulting approximations achieve a uniform reduction of free variables from three to two, and involve either modified Bessel functions or Airy functions. Explicit error bounds are available for all the approximations.

A new Reliable Numerical Algorithm Based on the First Kind of Bessel Functions to Solve Prandtl–Blasius Laminar Viscous Flow over a Semi-Infinite Flat Plate

2012 ◽  
Vol 67 (12) ◽  
pp. 665-673 ◽  
Author(s):  
Kourosh Parand ◽  
Mehran Nikarya ◽  
Jamal Amani Rad ◽  
Fatemeh Baharifard
Keyword(s):  
Viscous Flow ◽  
Flat Plate ◽  
Numerical Algorithm ◽  
Bessel Functions ◽  
Nonlinear Ordinary Differential Equation ◽  
Finite Domain ◽  
Algebraic Equations ◽  
Infinite Domain ◽  
Third Order ◽  
Domain Truncation

In this paper, a new numerical algorithm is introduced to solve the Blasius equation, which is a third-order nonlinear ordinary differential equation arising in the problem of two-dimensional steady state laminar viscous flow over a semi-infinite flat plate. The proposed approach is based on the first kind of Bessel functions collocation method. The first kind of Bessel function is an infinite series, defined on ℝ and is convergent for any x ∊ℝ. In this work, we solve the problem on semi-infinite domain without any domain truncation, variable transformation basis functions or transformation of the domain of the problem to a finite domain. This method reduces the solution of a nonlinear problem to the solution of a system of nonlinear algebraic equations. To illustrate the reliability of this method, we compare the numerical results of the present method with some well-known results in order to show the applicability and efficiency of our method.

Asymptotic expansions and converging factors V. Lommel, Struve, modified Struve, Anger and Weber functions, and integrals of ordinary and modified Bessel functions

1959 ◽  
Vol 249 (1257) ◽  
pp. 284-292 ◽  
Keyword(s):  
Asymptotic Expansions ◽  
Bessel Functions ◽  
Modified Bessel Functions ◽  
Lommel Functions ◽  
Special Cases

A theory of Lommel functions is developed, based upon the methods described in the first four papers (I to IV) of this series for replacing the divergent parts of asymptotic expansions by easily calculable series involving one or other of the four ‘basic converging factors’ which were investigated and tabulated in I. This theory is then illustrated by application to the special cases of Struve, modified Struve, Anger and Weber functions, and integrals of ordinary and modified Bessel functions.

(p, q)-Extended Bessel and Modified Bessel Functions of the First Kind

2017 ◽  
Vol 72 (1-2) ◽  
pp. 617-632 ◽  
Author(s):  
Dragana Jankov Maširević ◽  
Rakesh K. Parmar ◽  
Tibor K. Pogány
Keyword(s):  
Bessel Functions ◽  
Modified Bessel Functions
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