scholarly journals The Bessel Expansion of Fourier Integral on Finite Interval

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 607
Author(s):  
Yongxiong Zhou ◽  
Zhenyu Zhao
Keyword(s):  
Bessel Function ◽  
Numerical Experiments ◽  
Complex Analysis ◽  
Finite Interval ◽  
Fourier Integral ◽  
Type Method ◽  
Function Expansion ◽  
Oscillation Frequencies

In this paper, we further extend the Filon-type method to the Bessel function expansion for calculating Fourier integral. By means of complex analysis, this expansion is effective for all the oscillation frequencies. Namely, the errors of the expansion not only decrease as the order of the derivative increases, but also decrease rapidly as the frequency increases. Some numerical experiments are also presented to verify the effectiveness of the method.

scholarly journals Stabilised explicit Adams-type methods

2021 ◽  
pp. 82-98
Author(s):  
Vasily I. Repnikov ◽  
Boris V. Faleichik ◽  
Andrew V. Moisa
Keyword(s):  
Numerical Experiments ◽  
Step Method ◽  
Type Method ◽  
Constrained Optimisation ◽  
First Order ◽  
Error Constant ◽  
Stability Intervals ◽  
Multi Step Methods ◽  
First Order Methods ◽  
Accuracy And Stability

In this work we present explicit Adams-type multi-step methods with extended stability intervals, which are analogous to the stabilised Chebyshev Runge – Kutta methods. It is proved that for any k ≥ 1 there exists an explicit k-step Adams-type method of order one with stability interval of length 2k. The first order methods have remarkably simple expressions for their coefficients and error constant. A damped modification of these methods is derived. In the general case, to construct a k-step method of order p it is necessary to solve a constrained optimisation problem in which the objective function and p constraints are second degree polynomials in k variables. We calculate higher-order methods up to order six numerically and perform some numerical experiments to confirm the accuracy and stability of the methods.

On modeling column crystallizers and a Hermite predictor–corrector scheme for a system of integro-differential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Khaldoun El Khaldi ◽  
Nima Rabiei ◽  
Elias G. Saleeby
Keyword(s):  
Numerical Experiments ◽  
Main Part ◽  
Direct Method ◽  
Particle Agglomeration ◽  
Volterra Type ◽  
Type Method ◽  
Method Of Solution ◽  
System Of Integrodifferential Equations ◽  
Predictor Corrector ◽  
A Direct Method

Abstract Multistaged crystallization systems are used in the production of many chemicals. In this article, employing the population balance framework, we develop a model for a column crystallizer where particle agglomeration is a significant growth mechanism. The main part of the model can be reduced to a system of integrodifferential equations (IDEs) of the Volterra type. To solve this system simultaneously, we examine two numerical schemes that yield a direct method of solution and an implicit Runge–Kutta type method. Our numerical experiments show that the extension of a Hermite predictor–corrector method originally advanced in Khanh (1994) for a single IDE is effective in solving our model. The numerical method is presented for a generalization of the model which can be used to study and simulate a number of possible operating profiles of the column.

Bessel function expansion to reduce the calculation time and memory usage for cylindrical computer-generated holograms

2017 ◽  
Vol 56 (20) ◽  
pp. 5775 ◽  
Author(s):  
Yusuke Sando ◽  
Daisuke Barada ◽  
Boaz Jessie Jackin ◽  
Toyohiko Yatagai
Keyword(s):  
Bessel Function ◽  
Memory Usage ◽  
Calculation Time ◽  
Function Expansion ◽  
Computer Generated Holograms

scholarly journals A General Inertial Viscosity Type Method for Nonexpansive Mappings and Its Applications in Signal Processing

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 288 ◽  
Author(s):  
Yinglin Luo ◽  
Meijuan Shang ◽  
Bing Tan
Keyword(s):  
Signal Processing ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Type Method ◽  
Pseudocontractive Mappings ◽  
Inertia Parameters ◽  
Strictly Pseudocontractive Mappings

In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms and comparisons with existing algorithms are given to the demonstration of the efficiency of the proposed algorithms. The numerical results show that our algorithms are superior to some related algorithms.

scholarly journals On an integral transform

1988 ◽  
Vol 11 (4) ◽  
pp. 635-642
Author(s):  
D. Naylor
Keyword(s):  
Bessel Function ◽  
Power Function ◽  
Inversion Formula ◽  
Bessel Functions ◽  
Integral Transform ◽  
Finite Interval ◽  
Power Functions ◽  
Inversion Theorem ◽  
Eigenvalue Parameter

A formula of inversion is established for an integral transform whose kernel is the Bessel functionJu(kr)wherervaries over the finite interval(0,a)and the orderuis taken to be the eigenvalue parameter. When this parameter is large the Bessel function behaves for varyingrlike the power functionruand by relating the Bessel functions to their corresponding power functions the proof of the inversion formula can be reduced to one depending on the Mellin inversion theorem.

The Summation of a Fourier Integral of Finite Type

1926 ◽  
Vol 23 (4) ◽  
pp. 373-382 ◽  
Author(s):  
S. Pollard
Keyword(s):  
Finite Type ◽  
Generating Function ◽  
Finite Interval ◽  
Fourier Integral ◽  
Image Position

A Fourier integral will be described as of finite type if the range of integration of the integrals by means of which the coefficients in the Fourier integral are defined is a finite interval instead of the usual (−∞ ∞). Thus is of finite type (p, q), such that where ƒ(x) is the generating function of the series.

scholarly journals Modified Suliciu relaxation system and exact resolution of isolated shock waves

2014 ◽  
Vol 24 (05) ◽  
pp. 937-971 ◽  
Author(s):  
Christophe Chalons ◽  
Frederic Coquel
Keyword(s):  
Gas Dynamics ◽  
Numerical Experiments ◽  
Entropy Inequality ◽  
Riemann Solver ◽  
Gas Dynamics Equations ◽  
Pressure Relaxation ◽  
Type Method ◽  
Lipschitz Continuous ◽  
Shock Profiles ◽  
Exact Resolution

We present a new approximate Riemann solver (ARS) for the gas dynamics equations in Lagrangian coordinates and with general nonlinear pressure laws. The design of this new ARS relies on a generalized Suliciu pressure relaxation approach. It gives by construction the exact solutions for isolated entropic shocks and we prove that it is positive, Lipschitz-continuous and satisfies an entropy inequality. Finally, the ARS is used to develop either a classical entropy conservative Godunov-type method, or a Glimm-type (random sampling-based Godunov-type) method able to generate infinitely sharp discrete shock profiles. Numerical experiments are proposed to prove the validity of these approaches.

scholarly journals Application of Quasisubordination to Certain Classes of Meromorphic Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Syed Ghoos Ali Shah ◽  
Saqib Hussain ◽  
Akhter Rasheed ◽  
Zahid Shareef ◽  
Maslina Darus
Keyword(s):  
Bessel Function ◽  
Complex Analysis ◽  
Meromorphic Functions ◽  
Real Analysis ◽  
Real Functions

Inequalities play a fundamental role in many branches of mathematics and particularly in real analysis. By using inequalities, we can find extrema, point of inflection, and monotonic behavior of real functions. Subordination and quasisubordination are important tools used in complex analysis as an alternate of inequalities. In this article, we introduce and systematically study certain new classes of meromorphic functions using quasisubordination and Bessel function. We explore various inequalities related with the famous Fekete-Szego inequality. We also point out a number of important corollaries.

Sign in / Sign up

Export Citation Format

Share Document