scholarly journals Sharp inequality of three point Gauss—Legendre quadrature rule

2020 ◽  
Vol 39 (3) ◽  
pp. 639-649
Author(s):  
Artion Kashuri
Keyword(s):  
Quadrature Rule ◽  
Sharp Inequality ◽  
Legendre Quadrature

scholarly journals Gauss-Legendre Numerical Integrations over a Quadrilateral Element in Closed Form

1970 ◽  
Vol 46 (3) ◽  
pp. 399-405 ◽  
Author(s):  
MS Islam ◽  
G Saha ◽  
N Akter
Keyword(s):  
Closed Form ◽  
Coordinate Transformation ◽  
Stiffness Matrix ◽  
Quadrature Rule ◽  
Computational Time ◽  
Quadrilateral Element ◽  
Memory Space ◽  
The Matrix ◽  
Quadrilateral Finite Element ◽  
Legendre Quadrature

In this paper we investigate the stiffness matrix of a general quadrilateral element in closed form using n x n Gauss-Legendre quadrature rule. For this, we propose four types of nodal coordinate transformation. The terms of the matrix are divided into two groups, namely - diagonal and non-diagonal. Only one term (called leading) from each group is computed, and then the remaining fourteen terms are computed from these two leading terms exploited one of the proposed types of coordinate transformation. This leads us a great savings in computational time and memory space. In order to compute the matrix we use these transformations in two ways, and thus two algorithms are given to generate the matrix. Finally, numerical example is given to verify the effectiveness of the present formulation. Keywords: Gauss-Legendre quadrature; Numerical integration; Quadrilateral finite element; Stiffness matrix; Closed form. DOI: http://dx.doi.org/10.3329/bjsir.v46i3.9050 BJSIR 2011; 46(3): 399-405

scholarly journals A Mixed Quadrature Rule by Blending Clenshaw-Curtis and Gauss-Legendre Quadrature Rules for Approximate Evaluation of Real Definite Integrals

2012 ◽  
Vol 2 ◽  
pp. 10-15
Author(s):  
Anasuya Pati ◽  
Rajani B. Dash ◽  
Pritikanta Patra
Keyword(s):  
Quadrature Rule ◽  
Quadrature Rules ◽  
Approximate Evaluation ◽  
Definite Integrals ◽  
Legendre Quadrature

A mixed quadrature rule blending Clenshaw-Curtis five point rule and Gauss-Legendre three point rule is formed. The mixed rule has been tested and found to be more effective than that of its constituent Clenshaw-Curtis five point rule.

A new method for gravity modeling using tesseroids and 2D Gauss-Legendre quadrature rule

2019 ◽  
Vol 164 ◽  
pp. 53-64 ◽  
Author(s):  
Yiyuan Zhong ◽  
Zhengyong Ren ◽  
Chaojian Chen ◽  
Huang Chen ◽  
Zhi Yang ◽  
...  
Keyword(s):  
Quadrature Rule ◽  
New Method ◽  
Gravity Modeling ◽  
Legendre Quadrature

scholarly journals New error bounds for Gauss-Legendre quadrature rules

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1281-1293 ◽  
Author(s):  
Mohammad Masjed-Jamei
Keyword(s):  
Quadrature Formula ◽  
Error Bounds ◽  
Quadrature Rule ◽  
Order Derivative ◽  
Quadrature Rules ◽  
Linear Kernel ◽  
Large N ◽  
Interpolatory Quadrature ◽  
Integrand Function ◽  
Legendre Quadrature

It is well-known that the remaining term of any n-point interpolatory quadrature rule such as Gauss-Legendre quadrature formula depends on at least an n-order derivative of the integrand function, which is of no use if the integrand is not smooth enough and requires a lot of differentiation for large n. In this paper, by defining a specific linear kernel, we resolve this problemand obtain new bounds for the error of Gauss-Legendre quadrature rules. The advantage of the obtained bounds is that they do not depend on the norms of the integrand function. Some illustrative examples are given in this direction.

scholarly journals Approximate Solutions of Time Fractional Diffusion Wave Models

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 923 ◽  
Author(s):  
Abdul Ghafoor ◽  
Sirajul Haq ◽  
Manzoor Hussain ◽  
Poom Kumam ◽  
Muhammad Asif Jan
Keyword(s):  
Finite Difference ◽  
Wave Equations ◽  
Quadrature Rule ◽  
Approximate Solutions ◽  
Fractional Diffusion ◽  
Haar Wavelets ◽  
Test Problems ◽  
Algebraic Equations ◽  
Diffusion Wave ◽  
Wave Models

In this paper, a wavelet based collocation method is formulated for an approximate solution of (1 + 1)- and (1 + 2)-dimensional time fractional diffusion wave equations. The main objective of this study is to combine the finite difference method with Haar wavelets. One and two dimensional Haar wavelets are used for the discretization of a spatial operator while time fractional derivative is approximated using second order finite difference and quadrature rule. The scheme has an excellent feature that converts a time fractional partial differential equation to a system of algebraic equations which can be solved easily. The suggested technique is applied to solve some test problems. The obtained results have been compared with existing results in the literature. Also, the accuracy of the scheme has been checked by computing L 2 and L ∞ error norms. Computations validate that the proposed method produces good results, which are comparable with exact solutions and those presented before.

scholarly journals Quadrature Integration Techniques for Random Hyperbolic PDE Problems

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 160
Author(s):  
Rafael Company ◽  
Vera N. Egorova ◽  
Lucas Jódar
Keyword(s):  
Numerical Methods ◽  
Laplace Transform ◽  
Quadrature Rule ◽  
Inverse Laplace Transform ◽  
Process Time ◽  
Efficient Computation ◽  
Hyperbolic Pde ◽  
Numerical Convergence ◽  
Laplace Transform Technique ◽  
Integration Techniques

In this paper, we consider random hyperbolic partial differential equation (PDE) problems following the mean square approach and Laplace transform technique. Randomness requires not only the computation of the approximating stochastic processes, but also its statistical moments. Hence, appropriate numerical methods should allow for the efficient computation of the expectation and variance. Here, we analyse different numerical methods around the inverse Laplace transform and its evaluation by using several integration techniques, including midpoint quadrature rule, Gauss–Laguerre quadrature and its extensions, and the Talbot algorithm. Simulations, numerical convergence, and computational process time with experiments are shown.

Reliability analysis and state transfer scheduling optimization of degrading load-sharing system equipped with warm standby components

2021 ◽  
pp. 1748006X2110017
Author(s):  
Sheng-Jia Ruan ◽  
Yan-Hui Lin
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
High Reliability ◽  
Quadrature Rule ◽  
Load Sharing ◽  
Measurement Information ◽  
Model Parameters ◽  
Scheduling Optimization ◽  
State Transfer ◽  
Warm Standby

Standby redundancy can meet system safety requirements in industries with high reliability standards. To evaluate reliability of standby systems, failure dependency among components has to be considered especially when systems have load-sharing characteristics. In this paper, a reliability analysis and state transfer scheduling optimization framework is proposed for the load-sharing 1-out-of- N: G system equipped with M warm standby components and subject to continuous degradation process. First, the system reliability function considering multiple dependent components is derived in a recursive way. Then, a Monte Carlo method is developed and the closed Newton-Cotes quadrature rule is invoked for the system reliability quantification. Besides, likelihood functions are constructed based on the measurement information to estimate the model parameters of both active and standby components, whose degradation paths are modeled by the step-wise drifted Wiener processes. Finally, the system state transfer scheduling is optimized by the genetic algorithm to maximize the system reliability at mission time. The proposed methodology and its effectiveness are illustrated through a case study referring to a simplified aircraft hydraulic system.

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