Some new applications of truncated Gauss-Laguerre quadrature formulas

Mastroianni, G.; Monegato, Giovanni

doi:10.1007/s11075-008-9191-x

Cited by 14 publications

(3 citation statements)

References 8 publications

(19 reference statements)

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“…Solving the improper integral I by using analytical methods is difficult, so we need to solve this integral numerically. In [17], the authors applied the Gauss-Laquerre quadrature formulas directly. However, calculating the nodes and weights of the formula for large powers of polynomials leads to an increase of the arithmetic complexity of calculations.…”

Section: Introductionmentioning

confidence: 99%

A Valid Dynamical Control on the Reverse Osmosis System Using the CESTAC Method

et al. 2020

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The aim of this study is to present a novel method to find the optimal solution of the reverse osmosis (RO) system. We apply the Sinc integration rule with single exponential (SE) and double exponential (DE) decays to find the approximate solution of the RO. Moreover, we introduce the stochastic arithmetic (SA), the CESTAC method (Controle et Estimation Stochastique des Arrondis de Calculs) and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library instead of the mathematical methods based on the floating point arithmetic (FPA). Applying this technique, we would be able to find the optimal approximation, the optimal error and the optimal iteration of the method. The main theorems are proved to support the method analytically. Based on these theorems, we can apply a new stopping condition in the numerical procedure instead of the traditional absolute error. These theorems show that the number of common significant digits (NCSDs) of exact and approximate solutions are almost equal to the NCSDs of two successive approximations. The numerical results are obtained for both SE and DE Sinc integration rules based on the FPA and the SA. Moreover, the number of iterations for various ε are computed in the FPA. Clearly, the DE case is more accurate and faster than the SE for finding the optimal approximation, the optimal error and the optimal iteration of the RO system.

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Section: Introductionmentioning

confidence: 99%

A Valid Dynamical Control on the Reverse Osmosis System Using the CESTAC Method

et al. 2020

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“…Other methods use spline functions and wavelets [30,33,34], product integration [13,35], homotopy analysis techniques [36] homotopy perturbation and Adomian decomposition method [37,38], polynomial interpolation procedures and suboptimal trajectories [25,39], multigrid methods [13,40]. Nystrom techniques are used in [12,13,18,[41][42][43][44]. The iterative methods involve Newton procedures and the derived Broyden method can be found in [12,14,[45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of volterra functional integral equation by using cubic B‐spline scaling functions

Maleknejad

Mollapourasl

Mirzaei

2013

Numerical Methods Partial

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In this article, we consider a class of nonlinear functional integral equations which has rather general form and contains a lot of particular cases such as functional equations and nonlinear integral equations of Volterra type. We use a combination of a fixed point method and cubic semiorthogonal B‐spline scaling functions to solve the integral equation numerically. We provide an error analysis for the method which shows that the approximate solution converges to the exact solution. Some numerical results for several test problems are given to confirm the accuracy and the ease of implementation of the method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 699–722, 2014

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“…Other methods use spline functions and wavelets (see [5,46,47,50]), product integration (see [9,29]), homotopy analysis techniques (see [2]), homotopy perturbation and Adomian decomposition method (see [3] and [18]), polynomial interpolation procedures and suboptimal trajectories (see [22] and [26]), multigrid methods (see [9,39]). Nyström techniques are used in [8,9,15,16,28,48] and [58]. The iterative methods involve Newton procedures and the derived Broyden method and can be found in [8,10,30,37,38,57] and [58].…”

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confidence: 99%