Control of Dynamic Noise in Transcendental Julia and Mandelbrot Sets by Superior Iteration Method

2018 ◽  
Vol 7 (2) ◽  
pp. 48-59 ◽  
Author(s):  
Ketan Jha ◽  
Mamta Rani
Keyword(s):  
Iteration Method ◽  
Dynamic Noise ◽  
Different Types ◽  
Mandelbrot Sets

Researchers and scientists are attracted towards Julia and Mandelbrot sets constantly. They analyzed these sets intensively. Researchers have studied the perturbation in Julia and Mandelbrot sets which is due to different types of noises, but transcendental Julia and Mandelbrot sets remained ignored. The purpose of this article is to study the perturbation in transcendental Julia and Mandelbrot sets. Also, we made an attempt to control the perturbation in transcendental sets by using superior iteration method.

scholarly journals Behavior of the Correction Equations in the Jacobi–Davidson Method

2019 ◽  
Vol 2019 ◽  
pp. 1-4 ◽  
Author(s):  
Yuan Kong ◽  
Yong Fang
Keyword(s):  
Iteration Method ◽  
Convergence Property ◽  
Hermitian Matrices ◽  
Davidson Method ◽  
Different Types ◽  
Correction Equations

The Jacobi–Davidson iteration method is efficient for computing several eigenpairs of Hermitian matrices. Although the involved correction equation in the Jacobi–Davidson method has many developed variants, the behaviors of them are not clear for us. In this paper, we aim to explore, theoretically, the convergence property of the Jacobi–Davidson method influenced by different types of correction equations. As a by-product, we derive the optimal expansion vector, which imposed a shift-and-invert transform on a vector located in the prescribed subspace, to expand the current subspace.

scholarly journals VIM for Solving the Pollution Problem of a System of Lakes

2010 ◽  
Vol 2010 ◽  
pp. 1-6 ◽  
Author(s):  
J. Biazar ◽  
M. Shahbala ◽  
H. Ebrahimi
Keyword(s):  
Differential Equations ◽  
Iteration Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Environment Monitoring ◽  
System Of Differential Equations ◽  
Variational Iteration ◽  
Pollution Problem ◽  
Adomian Decomposition ◽  
Different Types

Pollution has become a very serious threat to our environment. Monitoring pollution is the first step toward planning to save the environment. The use of differential equations of monitoring pollution has become possible. In this paper the pollution problem of three lakes with interconnecting channels has been studied. The variational iteration method has been applied to compute an approximate solution of the system of differential equations, governing on the problem. Three different types of input models: sinusoidal, impulse, and step will be considered for monitoring the pollution in the lakes. The results are compared with those obtained by Adomian decomposition method. This comparison reveals that the variational iteration method is easier to be implemented.

Estimation of Dynamic Noise in Mandelbrot Map

2017 ◽  
Vol 7 (2) ◽  
pp. 1-20
Author(s):  
Ketan Jha ◽  
Mamta Rani
Keyword(s):  
Dynamic Noise ◽  
Fractal Image ◽  
Restoration Algorithm ◽  
Mandelbrot Sets

Julia and Mandelbrot sets have been studied continuously attracting fractal scientists since their creation. As a result, Julia and Mandelbrot sets have been analyzed intensively. In this article, researchers have studied the effect of noise on these sets and analyzed perturbation. Continuing the trend in this article, they analyze perturbation and find the corresponding amount of dynamic noise in the Mandelbrot map. Further, in order to recover a distorted fractal image, a restoration algorithm is presented.

Dynamic noise perturbed generalized superior Mandelbrot sets

2011 ◽  
Vol 67 (3) ◽  
pp. 1883-1891 ◽  
Author(s):  
Rashi Agarwal ◽  
Vishal Agarwal
Keyword(s):  
Dynamic Noise ◽  
Mandelbrot Sets

ANALYTICAL COMPARISON BETWEEN THE HOMOTOPY PERTURBATION METHOD AND VARIATIONAL ITERATION METHOD FOR DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

2008 ◽  
Vol 22 (23) ◽  
pp. 4041-4058 ◽  
Author(s):  
ZAID ODIBAT ◽  
SHAHER MOMANI
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Order ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Different Types

Comparison of homotopy perturbation method (HPM) and variational iteration method (VIM) is made, revealing that the two methods can be used as alternative and equivalent methods for obtaining analytic and approximate solutions for different types of differential equations of fractional order. Furthermore, the former is more general and powerful than the latter. Numerical results show that the two approaches are easy to implement and accurate when applied to differential equations of fractional order.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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