scholarly journals Higher Order Fibonacci Sequence and Series by Generalized Higher Order Variable Co-Efficient Difference Operator

10.26524/cm9 ◽  
2017 ◽  
Vol 1 (1) ◽  
pp. 112-122
Author(s):  
Sandra Pinelas ◽  
Mohan B ◽  
Britto Antony Xavier G
Keyword(s):  
Difference Operator ◽  
Fibonacci Sequence ◽  
Higher Order ◽  
Order Variable

scholarly journals Advanced fibonacci sequence and its sum by second order variable co-efficient difference operator

2021 ◽  
Vol 5 (2) ◽  
pp. 92-101
Author(s):  
Rajiniganth P ◽  
Britto Antony Xavier G
Keyword(s):  
Difference Operator ◽  
Fibonacci Sequence ◽  
Second Order ◽  
Order Difference ◽  
Order Variable

We introduce a second order difference operator with specific powers of variable co-efficient and its inverse in this study, which allows us to derive the (α1tr1, α2tr2 )-Fibonacci sequence and its summation. This series is known as the Fibonacci sequence with variable co-efficients (VCFS). On the sum of the terms of the variable co-efficient Fibonacci sequence, some theorems and intriguing findings are generated. To demonstrate our findings, appropriate instances arepresented.

Rogue wave solutions for the higher-order nonlinear Schrödinger equation with variable coefficients by generalized Darboux transformation

2016 ◽  
Vol 30 (10) ◽  
pp. 1650106 ◽  
Author(s):  
Hai-Qiang Zhang ◽  
Jian Chen
Keyword(s):  
Darboux Transformation ◽  
Variable Coefficient ◽  
Rogue Wave ◽  
Variable Coefficients ◽  
Higher Order ◽  
Optical Systems ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Order Variable ◽  
Generalized Darboux Transformation

In this paper, we study a higher-order variable coefficient nonlinear Schrödinger (NLS) equation, which plays an important role in the control of the ultrashort optical pulse propagation in nonlinear optical systems. Then, we construct a generalized Darboux transformation (GDT) for the higher-order variable coefficient NLS equation. The [Formula: see text]th order rogue wave solution is obtained by the iterative rule and it can be expressed by the determinant form. As application, we calculate rogue waves (RWs) from first- to fourth-order in accordance with different kinds of parameters. In particular, the dynamical properties and spatial-temporal structures of RWs are discussed and compared with Hirota equation through some figures.

scholarly journals Some Applications of Higher Order Generalized α− Difference Operator

10.26524/cm41 ◽  
2018 ◽  
Vol 2 (2) ◽  
pp. 80-88
Author(s):  
Gokulakrishnan S ◽  
Chandrasekar V
Keyword(s):  
Numerical Methods ◽  
Difference Operator ◽  
Higher Order ◽  
Discrete Version

In this paper, we derive the discrete version of the Bernoulli’s formula according to the generalized α- difference operator for negative `l ,and to find the sum of several type of arithmetic series in the field of Numerical Methods. Suitable example are provided to illustrate the main results.

scholarly journals Fibonacci Sequence and its Sum by Second Order Difference Operator with Polynomial Factorial

10.26524/cm36 ◽  
2018 ◽  
Vol 2 (2) ◽  
pp. 20-29
Author(s):  
Sandra Pinelas ◽  
Rajiniganth P
Keyword(s):  
Difference Operator ◽  
Fibonacci Sequence ◽  
Second Order ◽  
Order Difference

scholarly journals Fibonacci Sequence and Series by Second Order Difference Operator with Logarithmic Function

10.26524/cm39 ◽  
2018 ◽  
Vol 2 (2) ◽  
pp. 51-60
Author(s):  
Rajiniganth P ◽  
Britto Antony Xavier G
Keyword(s):  
Difference Operator ◽  
Fibonacci Sequence ◽  
Second Order ◽  
Logarithmic Function ◽  
Order Difference

scholarly journals Some Applications of Higher Order Generalized α− Difference Operator

10.26524/41 ◽  
2018 ◽  
Vol 2 (2) ◽  
pp. 80-88
Author(s):  
Gokulakrishnan S ◽  
Chandrasekar V
Keyword(s):  
Difference Operator ◽  
Higher Order

scholarly journals Block GLT Sequences: Matrix Functions and Engineering Application

2019 ◽  
Vol 35 ◽  
pp. 204-222
Author(s):  
Carlo Garoni ◽  
Stefano Serra-Capizzano
Keyword(s):  
Finite Element ◽  
Variable Coefficient ◽  
Eigenvalue Problems ◽  
Galerkin Approximation ◽  
Engineering Application ◽  
Higher Order ◽  
Matrix Functions ◽  
Hermitian Matrices ◽  
Systems Of Differential Equations ◽  
Order Variable

The theory of block generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the spectral distribution of block-structured matrices arising from the discretization of differential problems, with a special reference to systems of differential equations (DEs) and to the higher-order finite element or discontinuous Galerkin approximation of both scalar and vectorial DEs. In the present paper, the theory of block GLT sequences is extended by proving that $\{f(A_n)\}_n$ is a block GLT sequence as long as $f$ is continuous and $\{A_n\}_n$ is a block GLT sequence formed by Hermitian matrices. It is also provided a relevant application of this result to the computation of the distribution of the numerical eigenvalues obtained from the higher-order isogeometric Galerkin discretization of second-order variable-coefficient differential eigenvalue problems (a topic of interest not only in numerical analysis but also in engineering).

scholarly journals Higher-order variable-step algorithms adapted to the accurate numerical integration of perturbed oscillators

1998 ◽  
Vol 12 (5) ◽  
pp. 467 ◽  
Author(s):  
Jesús Vigo-Aguiar ◽  
José M. Ferrándiz
Keyword(s):  
Numerical Integration ◽  
Higher Order ◽  
Variable Step ◽  
Order Variable
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