scholarly journals A general recurrence relation for the weight-functions in Mühlbach–Neville–Aitken representations with application to WENO interpolation and differentiation

2012 ◽  
Vol 219 (8) ◽  
pp. 4133-4142 ◽  
Author(s):  
G.A. Gerolymos
Keyword(s):  
Recurrence Relation ◽  
Weight Functions ◽  
Weno Interpolation

scholarly journals On 2-orthogonal polynomials of Laguerre type

1999 ◽  
Vol 22 (1) ◽  
pp. 29-48 ◽  
Author(s):  
Khalfa Douak
Keyword(s):  
Differential Equation ◽  
Orthogonal Polynomials ◽  
Recurrence Relation ◽  
Generating Function ◽  
Order Differential Equation ◽  
Integral Representations ◽  
Weight Functions ◽  
Linear Functionals ◽  
Third Order ◽  
Recurrence Coefficients

Let{Pn}n≥0be a sequence of 2-orthogonal monic polynomials relative to linear functionalsω0andω1(see Definition 1.1). Now, let{Qn}n≥0be the sequence of polynomials defined byQn:=(n+1)−1P′n+1,n≥0. When{Qn}n≥0is, also, 2-orthogonal,{Pn}n≥0is called “classical” (in the sense of having the Hahn property). In this case, both{Pn}n≥0and{Qn}n≥0satisfy a third-order recurrence relation (see below). Working on the recurrence coefficients, under certain assumptions and well-chosen parameters, a classical family of 2-orthogonal polynomials is presented. Their recurrence coefficients are explicitly determined. A generating function, a third-order differential equation, and a differential-recurrence relation satisfied by these polynomials are obtained. We, also, give integral representations of the two corresponding linear functionalsω0andω1and obtain their weight functions which satisfy a second-order differential equation. From all these properties, we show that the resulting polynomials are an extention of the classical Laguerre's polynomials and establish a connection between the two kinds of polynomials.

Sebuah Generalisasi Baru Barisan Fibonacci-Lucas

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Musraini M Musraini M ◽  
Rustam Efendi ◽  
Rolan Pane ◽  
Endang Lily
Keyword(s):  
Recurrence Relation ◽  
Initial Conditions ◽  
Lucas Sequence ◽  
Binet’S Formula

Barisan Fibonacci dan Lucas telah digeneralisasi dalam banyak cara, beberapa dengan mempertahankan kondisi awal, dan lainnya dengan mempertahankan relasi rekurensi. Makalah ini menyajikan sebuah generalisasi baru barisan Fibonacci-Lucas yang didefinisikan oleh relasi rekurensi B_n=B_(n-1)+B_(n-2),n≥2 , B_0=2b,B_1=s dengan b dan s bilangan bulat  tak negatif. Selanjutnya, beberapa identitas dihasilkan dan diturunkan menggunakan formula Binet dan metode sederhana lainnya. Juga dibahas beberapa identitas dalam bentuk determinan.   The Fibonacci and Lucas sequence has been generalized in many ways, some by preserving the initial conditions, and others by preserving the recurrence relation. In this paper, a new generalization of Fibonacci-Lucas sequence is introduced and defined by the recurrence relation B_n=B_(n-1)+B_(n-2),n≥2, with ,  B_0=2b,B_1=s                          where b and s are non negative integers. Further, some identities are generated and derived by Binet’s formula and other simple methods. Also some determinant identities are discussed.

A Meshless Method Based on the Nonsingular Weight Functions for Elastoplastic Large Deformation Problems

2019 ◽  
Vol 11 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Fengbin Liu ◽  
Qiang Wu ◽  
Yumin Cheng
Keyword(s):  
Large Deformation ◽  
Numerical Solutions ◽  
Weak Form ◽  
Weight Functions ◽  
Computational Accuracy ◽  
Lagrange Formulation ◽  
Element Free Galerkin ◽  
Penalty Factor ◽  
Element Free ◽  
Large Deformation Problems

In this study, based on a nonsingular weight function, the improved element-free Galerkin (IEFG) method is presented for solving elastoplastic large deformation problems. By using the improved interpolating moving least-squares (IMLS) method to form the approximation function, and using Galerkin weak form based on total Lagrange formulation of elastoplastic large deformation problems to form the discretilized equations, which is solved with the Newton–Raphson iteration method, we obtain the formulae of the IEFG method for elastoplastic large deformation problems. In numerical examples, the influences of the penalty factor, scale parameter of influence domain and weight functions on the computational accuracy are analyzed, and the numerical solutions show that the IEFG method for elastoplastic large deformation problems has higher computational efficiency and accuracy.

scholarly journals New Convolutions with Hermite Weight Functions

2021 ◽  
Author(s):  
Luís Pinheiro Castro ◽  
Anabela Sousa Silva ◽  
Nguyen Minh Tuan
Keyword(s):  
Weight Functions

scholarly journals Stationary Non-equilibrium Solutions for Coagulation Systems

2021 ◽  
Vol 240 (2) ◽  
pp. 809-875
Author(s):  
Marina A. Ferreira ◽  
Jani Lukkarinen ◽  
Alessia Nota ◽  
Juan J. L. Velázquez
Keyword(s):  
Power Law ◽  
Source Term ◽  
Continuous Model ◽  
Stationary Solutions ◽  
Weight Functions ◽  
Equilibrium Solutions ◽  
Coagulation Rate ◽  
Diffusion Limited Aggregation ◽  
Coagulation Equations ◽  
Non Equilibrium

AbstractWe study coagulation equations under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. We consider both discrete and continuous coagulation equations, and allow for a large class of coagulation rate kernels, with the main restriction being boundedness from above and below by certain weight functions. The weight functions depend on two power law parameters, and the assumptions cover, in particular, the commonly used free molecular and diffusion limited aggregation coagulation kernels. Our main result shows that the two weight function parameters already determine whether there exists a stationary solution under the presence of a source term. In particular, we find that the diffusive kernel allows for the existence of stationary solutions while there cannot be any such solutions for the free molecular kernel. The argument to prove the non-existence of solutions relies on a novel power law lower bound, valid in the appropriate parameter regime, for the decay of stationary solutions with a constant flux. We obtain optimal lower and upper estimates of the solutions for large cluster sizes, and prove that the solutions of the discrete model behave asymptotically as solutions of the continuous model.

scholarly journals A reverse Hardy–Hilbert-type integral inequality involving one derivative function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Qian Chen ◽  
Bicheng Yang
Keyword(s):  
Integral Inequality ◽  
Beta Function ◽  
Equivalent Form ◽  
Constant Factor ◽  
Weight Functions ◽  
Derivative Function ◽  
The Best Possible Constant ◽  
Type Integral ◽  
Hilbert Type ◽  
Hilbert Integral

AbstractIn this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral inequality involving one derivative function and the beta function is obtained. The equivalent statements of the best possible constant factor related to several parameters are considered. The equivalent form, the cases of non-homogeneous kernel and some particular inequalities are also presented.

scholarly journals Extending the Applicability of a Two-Step Chord-Type Method for Non-Differentiable Operators

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 804
Author(s):  
Ioannis K. Argyros ◽  
Neha Gupta ◽  
J. P. Jaiswal
Keyword(s):  
Approximate Solution ◽  
Convergence Analysis ◽  
Banach Spaces ◽  
Recurrence Relation ◽  
Convergence Theorem ◽  
Local Convergence ◽  
Existence And Uniqueness ◽  
Numerical Illustration ◽  
Type Method ◽  
Local Convergence Analysis

The semi-local convergence analysis of a well defined and efficient two-step Chord-type method in Banach spaces is presented in this study. The recurrence relation technique is used under some weak assumptions. The pertinency of the assumed method is extended for nonlinear non-differentiable operators. The convergence theorem is also established to show the existence and uniqueness of the approximate solution. A numerical illustration is quoted to certify the theoretical part which shows that earlier studies fail if the function is non-differentiable.

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