Explanipedia

A Simple Method For Interpolating and Integrating Discontinuous Functions Open

E. S. Shoukralla · 2024

There are many scientific problems related to the topic of interpolation, especially for non-‎continuous functions, as well as the evaluating of the integrals of such non-continuous ‎‎functions. These needs appear clearly in the developmen…

Barycentric Lagrange interpolation method for solving Love’s integral equations Open

E. S. Shoukralla, B. M. Ahmed · 2023

Mathematics Computer science Physics

In this paper, we present a new simple method for solving two integral equations of Love’s type that have many applications, especially in electrostatic systems. The approach of the solution is based on an innovative technique using matrix…

Barycentric Lagrange Interpolation Method for Solving Love’s Integral Equations Open

E. S. Shoukralla, B. M. Ahmed · 2023

Mathematics Computer science Physics

‫ـــــ‬ In this paper, we presented a new simple method for solving two integral equations of Love’s type that have many applications, especially in electrostatic systems. The approach of the solution is based on an innovative technique us…

Barycentric Lagrange Interpolation in Matrix-Vector Versions for solving Love’s Integral Equations Open

E. S. Shoukralla · 2023

Mathematics Computer science Physics

In this paper, we solve two integral equations of Love’s type that have many applications, especially in electrostatic systems. The approach of the solution is based on an innovative technique using matrix algebra for the barycentric Lagra…

Barycentric Lagrange Interpolation Methods for Evaluating Singular Integrals Open

E. S. Shoukralla, B. M. Ahmed · 2022

Mathematics Computer science Materials science

We investigate new, straightforward methods for interpolating and integrating discontinuous single and two-variable real valued functions. The method is based on some modified matrix–vector barycentric Lagrange interpolation formulas. We d…

On The Studying of Contact Mechanics of a Flat Stamp Graded Coatings Using An Advanced Barycentric Lagrange Interpolation Formula Open

Ahmed Y. Sayed, Nermin Saber, E. S. Shoukralla · 2022

Mathematics Computer science Engineering

In this paper, the initial fracture in graded coatings under sliding rigid flat stamp contact loading is considered.This problem could be represented in the form of weakly singular Fredholm of the second kind.Shoukralla et al [1], made pro…

Interpolation method for solving Volterra integral equations with weakly singular kernel using an advanced barycentric Lagrange formula Open

E. S. Shoukralla, B. M. Ahmed, M. Sayed, Ahmed Shaker · 2022

Mathematics Computer science Physics

We presented an interpolation method for solving weakly singular Volterra integral equations of the second kind (SVK2). The method based on the barycentric Lagrange interpolation.. For the chosen nodes of the two singular kernel variables,…

Safe Microwave Inactivation of Airborne Viruses Using Compact Smart Antenna Open

Kyrillos Youssef, E. S. Shoukralla, Vivianne K. Hanna, Ahmed S. Elkorany · 2021

Computer science Environmental science Engineering

The coronavirus disease 2019 (COVID-19) that broke out on December 2019 spread speedily throughout the world, resulting in serious economic problems and increasing the mortality rate. Preceding research illustrated that one of the main rou…

Computational Method for Solving Weakly Singular Fredholm Integral Equations of the Second Kind using an Advanced Barycentric Lagrange Interpolation Formula Open

E. S. Shoukralla, Nermin Saber, Ahmed Y. Sayed · 2021

Mathematics Physics

In this study, we applied an advanced barycentric Lagrange interpolation formula to find the interpolate solutions of weakly singular ‎Fredholm integral equations of the ‎second kind. The kernel is ‎interpolated twice concerning ‎both vari…

Shifted Legendre Polynomials For Solving Second Kind Fredholm Integral Equations Open

E. S. Shoukralla, H. A. El-Gohary, Michael A. Morgan · 2021

Mathematics Physics Materials science

—in this paper, present a computational method for solving Fredholm integral equations of the second kind. The method based on the application of the shifted Legendre polynomials in matrix forms. We create a technique for extracting the Le…

Interpolation Method for Solving Weakly Singular Integral Equations of the Second Kind Open

E. S. Shoukralla · 2021

Mathematics Computer science Materials science

We establish a new straightforward interpolation method for solving linear Volterra integral ‎‎equations with weakly singular kernels. The proposed method is fundamentally different from all other published methods for solving this type of…

Barycentric - Maclaurin Interpolation Method for Solving Volterra Integral Equations of the Second Kind Open

E. S. Shoukralla, H. A. El-Gohary, Basma Magdy · 2020

Mathematics Computer science

nd d K Ki in nd d

Barycentric Lagrange interpolation for solving Volterra integral equations of the second kind Open

E. S. Shoukralla, H. A. El-Gohary, B. M. Ahmed · 2020

Mathematics Computer science Physics

An improved version of Barycentric Lagrange interpolation with uniformly spaced interpolation nodes is established and applied to solve Volterra integral equations of the second kind. The given data function and the unknown functions are t…

Numerical Solutions of Volterra Integral Equations of the Second Kind using Lagrange interpolation via the Vandermonde matrix Open

E. S. Shoukralla, B. M. Ahmed · 2020

Mathematics Computer science Physics

A new method is established for solving Volterra integral equations of the second kind using Lagrange interpolation through the Vandermonde approach. The goal is to minimize the interpolation errors of the high-degree polynomials on equidi…

Numerical Solutions of Volterra Integral Equations of the Second Kind Using Barycentric Lagrange with Chebyshev Interpolation Open

E. S. Shoukralla, B. M. Ahmed · 2019

Mathematics Computer science Physics

The Barycentric Lagrange interpolation with non-uniformly spaced Chebyshev interpolation nodes has been modified and re-configured in a new formula to solve Volterra integral equations of the second kind. To avoid the application of the co…

A MATRIX ITERATIVE TECHNIQUE FOR THE SOLUTION OF FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND Vol. 4(1) Jan. 2016, No. 19, pp. 192-196 E. S. SHOUKRALLA, S. A. EL-SERAFI AND NERMEIN A. SABER Open

E. S. Shoukralla, S. El-Serafi, N.R. Saber · 2016

Mathematics Materials science

A Matrix Iterative Algorithm is given for the approximate solution of Fredholm integral equations of the second kind.The Algorithm modifies the ideas of iterated kernels via Hilbert matrix.Thus reducing the required solution so that only o…

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