NOTES ON NONNEGATIVE CONVERGENT SERIES

1992 ◽  
Vol 18 (2) ◽  
pp. 480
Author(s):  
Biró
Keyword(s):  
Convergent Series

HOMOTOPY ANALYSIS METHOD TO SOLVE BOUSSINESQ EQUATIONS

2015 ◽  
Vol 10 (3) ◽  
pp. 2825-2833
Author(s):  
Achala Nargund ◽  
R Madhusudhan ◽  
S B Sathyanarayana
Keyword(s):  
Homotopy Analysis Method ◽  
Degrees Of Freedom ◽  
Initial Approximation ◽  
Boussinesq Equations ◽  
Convergent Series ◽  
Boussinesq System ◽  
Analysis Method ◽  
Analytical Technique ◽  
Homotopy Analysis ◽  
Region Of Convergence

In this paper, Homotopy analysis method is applied to the nonlinear coupleddifferential equations of classical Boussinesq system. We have applied Homotopy analysis method (HAM) for the application problems in [1, 2, 3, 4]. We have also plotted Domb-Sykes plot for the region of convergence. We have applied Pade for the HAM series to identify the singularity and reflect it in the graph. The HAM is a analytical technique which is used to solve non-linear problems to generate a convergent series. HAM gives complete freedom to choose the initial approximation of the solution, it is the auxiliary parameter h which gives us a convenient way to guarantee the convergence of homotopy series solution. It seems that moreartificial degrees of freedom implies larger possibility to gain better approximations by HAM.

On Commutation Properties of the Composition Relation of Convergent and Divergent Permutations (Part I)

2014 ◽  
Vol 58 (1) ◽  
pp. 13-22
Author(s):  
Roman Wituła ◽  
Edyta Hetmaniok ◽  
Damian Słota
Keyword(s):  
Finite Order ◽  
Convergent Series ◽  
The Other ◽  
Other Hand ◽  
The Family ◽  
Composition Relation ◽  
The Continuum

Abstract In the paper we present the selected properties of composition relation of the convergent and divergent permutations connected with commutation. We note that a permutation on ℕ is called the convergent permutation if for each convergent series ∑an of real terms, the p-rearranged series ∑ap(n) is also convergent. All the other permutations on ℕ are called the divergent permutations. We have proven, among others, that, for many permutations p on ℕ, the family of divergent permutations q on ℕ commuting with p possesses cardinality of the continuum. For example, the permutations p on ℕ having finite order possess this property. On the other hand, an example of a convergent permutation which commutes only with some convergent permutations is also presented.

scholarly journals Using GEDI Waveforms for Improved TanDEM-X Forest Height Mapping: A Combined SINC + Legendre Approach

2021 ◽  
Vol 13 (15) ◽  
pp. 2882
Author(s):  
Hao Chen ◽  
Shane R. Cloude ◽  
Joanne C. White
Keyword(s):  
High Resolution ◽  
Forest Canopy ◽  
Test Site ◽  
Convergent Series ◽  
Canopy Height ◽  
Ecosystem Dynamics ◽  
Sinc Function ◽  
Vertical Profiles ◽  
Legendre Series ◽  
Vertical Profiling

In this paper, we consider a new method for forest canopy height estimation using TanDEM-X single-pass radar interferometry. We exploit available information from sample-based, space-borne LiDAR systems, such as the Global Ecosystem Dynamics Investigation (GEDI) sensor, which offers high-resolution vertical profiling of forest canopies. To respond to this, we have developed a new extended Fourier-Legendre series approach for fusing high-resolution (but sparsely spatially sampled) GEDI LiDAR waveforms with TanDEM-X radar interferometric data to improve wide-area and wall-to-wall estimation of forest canopy height. Our key methodological development is a fusion of the standard uniform assumption for the vertical structure function (the SINC function) with LiDAR vertical profiles using a Fourier-Legendre approach, which produces a convergent series of approximations of the LiDAR profiles matched to the interferometric baseline. Our results showed that in our test site, the Petawawa Research Forest, the SINC function is more accurate in areas with shorter canopy heights (<~27 m). In taller forests, the SINC approach underestimates forest canopy height, whereas the Legendre approach avails upon simulated GEDI forest structural vertical profiles to overcome SINC underestimation issues. Overall, the SINC + Legendre approach improved canopy height estimates (RMSE = 1.29 m) compared to the SINC approach (RMSE = 4.1 m).

The Korteweg-de Vries equation and water waves. Solutions of the equation. Part 1

1973 ◽  
Vol 59 (4) ◽  
pp. 721-736 ◽  
Author(s):  
Harvey Segur
Keyword(s):  
Water Waves ◽  
Large Time ◽  
Vries Equation ◽  
Asymptotic Properties ◽  
Series Representation ◽  
Convergent Series ◽  
Asymptotic Results ◽  
De Vries ◽  
Method Of Solution

The method of solution of the Korteweg–de Vries equation outlined by Gardneret al.(1967) is exploited to solve the equation. A convergent series representation of the solution is obtained, and previously known aspects of the solution are related to this general form. Asymptotic properties of the solution, valid for large time, are examined. Several simple methods of obtaining approximate asymptotic results are considered.

The Approximate Analytical Solution of the MHD Flow of a Power-Law Fluid

2013 ◽  
Vol 431 ◽  
pp. 198-201
Author(s):  
Jing Zhu ◽  
Lian Cun Zheng
Keyword(s):  
Differential Equations ◽  
Power Law ◽  
Velocity Ratio ◽  
Mhd Flow ◽  
Convergent Series ◽  
Analysis Method ◽  
Governing System ◽  
Homotopy Analysis ◽  
Incompressible Mhd ◽  
Good Agreement

This paper presents a theoretical analysis for the incompressible MHD stagnation-point flows of a Non-Newtonian Fluid over stretching sheets.The governing system of partial differential equations is first transformed into a system of dimensionless ordinary differential equations. By using the homotopy analysis method, a convergent series solution is obtained. The reliability and efficiency of series solutions are illustrated by good agreement with numerical results in the literature.Besides, the effects of the power-law indexthe magnetic field parameter and velocity ratio parameter on the flow are investigated.

scholarly journals Bounds and algorithms for the -Bessel function of imaginary order

2013 ◽  
Vol 16 ◽  
pp. 78-108 ◽  
Author(s):  
Andrew R. Booker ◽  
Andreas Strömbergsson ◽  
Holger Then
Keyword(s):  
Bessel Function ◽  
Convergent Series ◽  
Steepest Descent ◽  
Modified Bessel Function ◽  
Software Library ◽  
Asymptotic Bounds ◽  
Mixed Derivatives ◽  
Rigorous Computation ◽  
Working Out ◽  
Precise Asymptotic

AbstractUsing the paths of steepest descent, we prove precise bounds with numerical implied constants for the modified Bessel function${K}_{ir} (x)$of imaginary order and its first two derivatives with respect to the order. We also prove precise asymptotic bounds on more general (mixed) derivatives without working out numerical implied constants. Moreover, we present an absolutely and rapidly convergent series for the computation of${K}_{ir} (x)$and its derivatives, as well as a formula based on Fourier interpolation for computing with many values of$r$. Finally, we have implemented a subset of these features in a software library for fast and rigorous computation of${K}_{ir} (x)$.

Analysis of thermally stratified radiative flow of Sutterby fluid with mixed convection

2021 ◽  
pp. 095440622110078
Author(s):  
Saif-ur- Rehman ◽  
Nazir Ahmad Mir ◽  
Muhammad Farooq ◽  
Naila Rafiq ◽  
Shakeel Ahmad
Keyword(s):  
Mixed Convection ◽  
Convergent Series ◽  
Radiation Parameter ◽  
Boundary Layer Approximation ◽  
Similar Relation ◽  
Opposite Behavior ◽  
Velocity Increments ◽  
Transport Analysis ◽  
Convection Parameter ◽  
Linear Pdes

In this attempt, we investigate the mixed convection in Sutterby fluid flow based on boundary layer approximation. Heat transport analysis is composed of stratification and thermal radiative phenomena. The system of non-linear PDEs is transformed into coupled ODEs. Convergent series approximations are evaluated via homotopic technique. Influence of various pertinent parameters is sketched and graphically analyzed. It is found that horizontal velocity increments for higher mixed convection parameter. The radiation parameter has a similar relation with temperature whereas the stratification parameter shows opposite behavior for temperature field.

scholarly journals On Domain of Nörlund Sequences

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 268 ◽  
Author(s):  
Kuddusi Kayaduman ◽  
Fevzi Yaşar
Keyword(s):  
Banach Space ◽  
Bounded Variation ◽  
Sequence Space ◽  
Convergent Series ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Nörlund Matrix ◽  
Inclusion Relations ◽  
The Matrix ◽  
New Space

In 1978, the domain of the Nörlund matrix on the classical sequence spaces lp and l∞ was introduced by Wang, where 1 ≤ p < ∞. Tuğ and Başar studied the matrix domain of Nörlund mean on the sequence spaces f0 and f in 2016. Additionally, Tuğ defined and investigated a new sequence space as the domain of the Nörlund matrix on the space of bounded variation sequences in 2017. In this article, we defined new space and and examined the domain of the Nörlund mean on the bs and cs, which are bounded and convergent series, respectively. We also examined their inclusion relations. We defined the norms over them and investigated whether these new spaces provide conditions of Banach space. Finally, we determined their α­, β­, γ­duals, and characterized their matrix transformations on this space and into this space.

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