1,721,014 research outputs found
Supplemental Material - Stability analysis for a tripled system of fractional pantograph differential equations with nonlocal conditions
No full textSupplemental Material for Stability analysis for a tripled system of fractional pantograph differential equations with nonlocal conditions by Hasanen A Hammad, Rashwan A Rashwan, A Nafea, Mohammad Esmael Samei and Samad Noeiaghdam in Journal of Vibration and Control</p
P A NUMERICAL SOLUTION OF N -TH ORDER FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS BY INTEGRAL MEAN VALUE THEOREM METHOD
No full textAbstract: In this paper, a new and robust semi-analytical method for solving n-th order Fredholm integro-differential equations is proposed. The main idea in this method is applying the mean value theorem for integrals. This method changing the problems to system of algebraic equations so by solving this system we obtain approximate solution. By present some examples and plot the error function and comparison between exact and approximate solution, we show the ability, simplicity and effectiveness of this method
Some perturbed versions of the generalized trapezoid type inequalities for twice differentiable functions
No full text
Advantages of the Discrete Stochastic Arithmetic to Validate the Results of the Taylor Expansion Method to Solve the Generalized Abel’s Integral Equation
No full textThe aim of this paper is to apply the Taylor expansion method to solve the first and second kinds Volterra integral equations with Abel kernel. This study focuses on two main arithmetics: the FPA and the DSA. In order to apply the DSA, we use the CESTAC method and the CADNA library. Using this method, we can find the optimal step of the method, the optimal approximation, the optimal error, and some of numerical instabilities. They are the main novelties of the DSA in comparison with the FPA. The error analysis of the method is proved. Furthermore, the main theorem of the CESTAC method is presented. Using this theorem we can apply a new termination criterion instead of the traditional absolute error. Several examples are approximated based on the FPA and the DSA. The numerical results show the applications and advantages of the DSA than the FPA
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
A Novel Method for Solving Second Kind Volterra Integral Equations with Discontinuous Kernel
No full textLoad leveling problems and energy storage systems can be modeled in the form of Volterra integral equations (VIE) with a discontinuous kernel. The Lagrange–collocation method is applied for solving the problem. Proving a theorem, we discuss the precision of the method. To control the accuracy, we apply the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library. For this aim, we apply discrete stochastic mathematics (DSA). Using this method, we can control the number of iterations, errors and accuracy. Additionally, some numerical instabilities can be identified. With the aid of this theorem, a novel condition is used instead of the traditional conditions
Dynamical Strategy to Control the Accuracy of the Nonlinear Bio-Mathematical Model of Malaria Infection
No full textThis study focuses on solving the nonlinear bio-mathematical model of malaria infection. For this aim, the HATM is applied since it performs better than other methods. The convergence theorem is proven to show the capabilities of this method. Instead of applying the FPA, the CESTAC method and the CADNA library are used, which are based on the DSA. Applying this method, we will be able to control the accuracy of the results obtained from the HATM. Also the optimal results and the numerical instabilities of the HATM can be obtained. In the CESTAC method, instead of applying the traditional absolute error to show the accuracy, we use a novel condition and the CESTAC main theorem allows us to do that. Plotting several ℏ-curves the regions of convergence are demonstrated. The numerical approximations are obtained based on both arithmetics
A Novel Approach for Improving Reverse Osmosis Model Accuracy: Numerical Optimization for Water Purification Systems
No full textThe primary objective of this study is to present a new technique and library designed to validate the outcomes of numerical methods used for addressing various issues. This paper specifically examines the reverse osmosis (RO) model, a well-known water purification system. A crucial aspect of this problem involves solving an integral that is part of the overall solution. This integral is handled using one of the quadrature integration methods, with a focus on Romberg integration in this study. To manage the number of iterations, as well as to ensure accuracy and minimize errors, we employ the CESTAC method (Controle et Estimation Stochastique des Arrondis de Calculs) alongside the CADNA (Control of Accuracy and Debugging for Numerical Applications) library. By implementing this approach, we aim to achieve not only optimal results, but also the best method step and minimal error, and we aim to address numerical instabilities. The results show that only 16 iterations of the Romberg integration rule will be enough to find the approximate solutions.To demonstrate the efficacy and precision of our proposed method, we conducted two comprehensive comparative studies with the Sinc integration. The first study compares the optimal iteration count, optimal approximation, and optimal error between the single and double exponential decay methods and the Romberg integration technique. The second study evaluates the number of iterations required for convergence within various predefined tolerance values. The findings from both studies consistently indicate that our method outperforms the Sinc integration in terms of computational efficiency. Additionally, these comparative analyses highlight the potential of our approach as a reliable and effective tool for numerical integration
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