• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.911-925
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• 1997

We derive quadrature formulas for approximating wavelet coefficients for smooth functions from equally spaced point values with arbitrarily high degree of accuracy. Wa also estimate the error of quadrature formulas.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.179-192
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• 1997

An algorithm to get an optimal choice for the number of symmetric quadrature points is given to find symmetric quadrature points is given to find symmetric quadrature for-mulas over a unit disk with a minimal number of points even when a high degree of polynomial precision is required. The symmetric quad-rature formulas for numerical integration over a unit disk of complete polynomial functions up to degree 19 are presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.1
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• pp.127-135
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• 1999

An inequality of Ostrowski's type for monotonous nondecreasing mappings is given. Applications for quadrature formulas are pointed out.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.65-79
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• 2007

An optimal 3-point quadrature formula of closed type is derived. It is shown that the optimal quadrature formula has a better error bound than the well-known Simpson's rule. A corrected formula is also considered. Various error inequalities for these formulas are established. Applications in numerical integration are given.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1195-1209
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• 2009

In this paper, we point out some errors in a recent paper by Cordero and Torregrosa [7]. We prove the convergence of the variants of Newton's method for solving the system of nonlinear equations using two different approaches. Several examples are given, which illustrate the cubic convergence of these methods and verify the theoretical results.

• Journal of Electrical Engineering and Technology
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• v.10 no.3
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• pp.1188-1200
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• 2015

A unified numerical method for computing the quadrature weights, integration matrix, and differentiation matrix is newly developed in this study. For this purpose, a spline-like interpolation using piecewise continuous polynomials is converted into a global spline interpolation formula, with which the quadrature formulas can be derived from integration and differentiation of the transformed function in an exact manner. To prove the usefulness of the suggested approach, both the Lagrange and tension spline interpolations are represented in exactly the same form as global spline interpolation. The applicability of the proposed method on arbitrary nodes is illustrated using two different sets of nodes. A series of validations using three test functions is conducted to show the flexibility in selecting computational nodes with the present method.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.177-193
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• 2022

The main aim of this paper is to introduce a new generalization of the Wright series in two variables, which is expressed in terms of Hermite polynomials. The properties of the freshly defined function involving its auxiliary functions and the integral representations are established. Furthermore, a Gauss-Hermite quadrature and Gaussian quadrature formulas have been established to evaluate some integral representations of our main results and compare them with our theoretical evaluations using graphical simulations.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.205-228
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• 2005

Let I(f) be the integral defined by : $I(f) = \int\limits_{a}^{b} f(x)w(x)dx$ with f a given function, w a nonclassical weight function and [a, b] an interval of IR (of finite or infinite length). We propose to calculate the approximate value of I(f) by using a new scheme for deriving a non-linear system, satisfied by the three-term recurrence coefficients of semi-classical orthogonal polynomials. Finally we studies the Stability and complexity of this scheme.

• Structural Engineering and Mechanics
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• v.33 no.6
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• pp.747-763
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• 2009

In this work, the linear vibration characteristics of $90^{\circ}$ pipe bends and their cylindrical and toroidal shell components are studied. The finite element method, based on shear-deformation shell elements, is used to carry out a vibration analysis of metallic multiple $90^{\circ}$ mitred pipe bends. Single, double, and triple mitred bends are considered, as well as a smooth bend. Sample natural frequencies and mode shapes are given. To validate the procedure, comparison of the natural frequencies is made with existing results for cylindrical and toroidal shells. The influence of the multiplicity of the bend, the boundary conditions, and the various geometric parameters on the natural frequency is described. The differential quadrature method, based on classical shell theory, is used to study the vibration of components of these bends. Regression formulas are derived for cylindrical shells (straight pipes) with one or two oblique edges, and for sectorial toroidal shells (curved pipes, pipe elbows). Two types of support are considered for each case. The results given provide information about the vibration characteristics of pipe bends over a wide range of the geometric parameters.

• Advances in nano research
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• v.12 no.1
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• pp.37-47
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• 2022

In this paper, the non-linear static analysis of Timoshenko nanobeams consisting of bi-directional functionally graded material (BFGM) with immovable ends is investigated. The scratching in the FG nanobeam mid-plane, is the source of nonlinearity of the bending problems. The nonlocal theory is used to investigate the non-linear static deflection of nanobeam. In order to simplify the formulation, the problem formulas is derived according to the physical middle surface. The Hamilton principle is employed to determine governing partial differential equations as well as boundary conditions. Moreover, the differential quadrature method (DQM) and direct iterative method are applied to solve governing equations. Present results for non-linear static deflection were compared with previously published results in order to validate the present formulation. The impacts of the nonlocal factors, beam length and material property gradient on the non-linear static deflection of BFG nanobeams are investigated. It is observed that these parameters are vital in the value of the non-linear static deflection of the BFG nanobeam.