scholarly journals Quadrature rules with an even number of multiple nodes and a maximal trigonometric degree of exactness

Filomat ◽  
2015 ◽  
Vol 29 (10) ◽  
pp. 2239-2255 ◽  
Author(s):  
Tatjana Tomovic ◽  
Marija Stanic
Keyword(s):  
Numerical Method ◽  
Trigonometric Polynomials ◽  
Quadrature Rules ◽  
Numerical Examples ◽  
Degree Of Exactness ◽  
Interpolatory Quadrature

This paper is devoted to the interpolatory quadrature rules with an even number of multiple nodes, which have the maximal trigonometric degree of exactness. For constructing of such quadrature rules we introduce and consider the so-called s- and ?-orthogonal trigonometric polynomials. We present a numerical method for construction of mentioned quadrature rules. Some numerical examples are also included.

scholarly journals Multiple orthogonality in the space of trigonometric polynomials of semi-integer degree

Filomat ◽  
2015 ◽  
Vol 29 (10) ◽  
pp. 2227-2237
Author(s):  
Marija Stanic ◽  
Tatjana Tomovic
Keyword(s):  
Numerical Method ◽  
Recurrence Relations ◽  
Trigonometric Polynomials ◽  
Quadrature Rules ◽  
Numerical Examples ◽  
Optimal Set ◽  
Numer Math ◽  
Theoretical Results

In this paper we consider multiple orthogonal trigonometric polynomials of semi-integer degree, which are necessary for constructing of an optimal set of quadrature rules with an odd number of nodes for trigonometric polynomials in Borges? sense [Numer. Math. 67 (1994) 271-288]. We prove that such multiple orthogonal trigonometric polynomials satisfy certain recurrence relations and present numerical method for their construction, as well as for construction of mentioned optimal set of quadrature rules. Theoretical results are illustrated by some numerical examples.

scholarly journals Trigonometric multiple orthogonal polynomials of semi-integer degree and the corresponding quadrature formulas

2014 ◽  
Vol 96 (110) ◽  
pp. 211-226 ◽  
Author(s):  
Gradimir Milovanovic ◽  
Marija Stanic ◽  
Tatjana Tomovic
Keyword(s):  
Orthogonal Polynomials ◽  
Trigonometric Polynomials ◽  
Quadrature Rules ◽  
Quadrature Formulas ◽  
Numerical Examples ◽  
Multiple Orthogonal Polynomials ◽  
Optimal Set ◽  
Numer Math ◽  
Theoretical Results

An optimal set of quadrature formulas with an odd number of nodes for trigonometric polynomials in Borges? sense [Numer. Math. 67 (1994), 271-288], as well as trigonometric multiple orthogonal polynomials of semi-integer degree are defined and studied. The main properties of such a kind of orthogonality are proved. Also, an optimal set of quadrature rules is characterized by trigonometric multiple orthogonal polynomials of semiinteger degree. Finally, theoretical results are illustrated by some numerical examples.

scholarly journals Numerical method of identification of an unknown source term in a heat equation

2002 ◽  
Vol 8 (2) ◽  
pp. 161-168 ◽  
Author(s):  
Afet Golayoğlu Fatullayev
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Numerical Method ◽  
Minimization Problem ◽  
Unknown Function ◽  
Source Term ◽  
Numerical Procedure ◽  
Numerical Examples ◽  
Unknown Source

A numerical procedure for an inverse problem of identification of an unknown source in a heat equation is presented. Approach of proposed method is to approximate unknown function by polygons linear pieces which are determined consecutively from the solution of minimization problem based on the overspecified data. Numerical examples are presented.

Application of Bernoulli wavelet method to solve a system of fuzzy integral equations

2018 ◽  
Vol 9 (1-2) ◽  
pp. 16-27 ◽  
Author(s):  
Mohamed Abdel- Latif Ramadan ◽  
Mohamed R. Ali
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
Bernoulli Polynomials ◽  
Approximate Solutions ◽  
Fredholm Integral Equations ◽  
Fuzzy Integral ◽  
Algebraic Equations ◽  
Wavelet Method ◽  
Numerical Examples ◽  
Bernoulli Wavelet

In this paper, an efficient numerical method to solve a system of linear fuzzy Fredholm integral equations of the second kind based on Bernoulli wavelet method (BWM) is proposed. Bernoulli wavelets have been generated by dilation and translation of Bernoulli polynomials. The aim of this paper is to apply Bernoulli wavelet method to obtain approximate solutions of a system of linear Fredholm fuzzy integral equations. First we introduce properties of Bernoulli wavelets and Bernoulli polynomials, then we used it to transform the integral equations to the system of algebraic equations. The error estimates of the proposed method is given and compared by solving some numerical examples.

A NUMERICAL METHOD FOR 1D TIME-DEPENDENT SCHRÖDINGER EQUATION USING RADIAL BASIS FUNCTIONS

2013 ◽  
Vol 10 (02) ◽  
pp. 1341010 ◽  
Author(s):  
TONGSONG JIANG ◽  
ZHAOLIN JIANG ◽  
JOSEPH KOLIBAL
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Radial Basis Functions ◽  
Finite Difference Scheme ◽  
Good Accuracy ◽  
Basis Functions ◽  
Time Dependent ◽  
Numerical Examples ◽  
Radial Basis

This paper proposes a new numerical method to solve the 1D time-dependent Schrödinger equations based on the finite difference scheme by means of multiquadrics (MQ) and inverse multiquadrics (IMQ) radial basis functions. The numerical examples are given to confirm the good accuracy of the proposed methods.

scholarly journals A Numerical Method for Lane-Emden Equations Using Hybrid Functions and the Collocation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Changqing Yang ◽  
Jianhua Hou
Keyword(s):  
Differential Equation ◽  
Numerical Method ◽  
Collocation Method ◽  
Chebyshev Polynomials ◽  
Initial Value Problems ◽  
Algebraic Equations ◽  
Initial Value ◽  
Numerical Examples ◽  
Hybrid Functions ◽  
Block Pulse Functions

A numerical method to solve Lane-Emden equations as singular initial value problems is presented in this work. This method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area of differential equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

Direct Nondestructive Algorithm for Shape Defects Evaluation

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Sebastián Ossandón ◽  
José Klenner ◽  
Camilo Reyes
Keyword(s):  
Boundary Element Method ◽  
Nondestructive Evaluation ◽  
Numerical Method ◽  
Boundary Element ◽  
Stability And Convergence ◽  
Nondestructive Analysis ◽  
Numerical Examples ◽  
Galerkin Boundary Element Method ◽  
Shape Differentiation ◽  
Analysis Stability

An efficient numerical method based on a rigorous integral formulation is used to calculate precisely the acoustic eigenvalues of complex shaped objects and their associated eigenvectors. These eigenvalues are obtained and later used in acoustic nondestructive evaluation. This study uses the eigenvalues to implement a simple acoustic shape differentiation algorithm that is the key in our direct nondestructive analysis. Stability and convergence of the Galerkin boundary element method used herein are discussed. Finally, some numerical examples are shown.

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