M. GUECHI Somia

MCB

Directory of teachers

Department

Departement of MECHANICAL ENGINEERING

Research Interests

Mathématiques et applications

Contact Info

University of M'Sila, Algeria

Email : somia.guechi@univ-msila.dz

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Recent Publications

2024-08-01

La revue des sciences appliquées

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Citation

M. GUECHI Somia, (2024-08-01), "La revue des sciences appliquées", [national] , Ahmed Rhif (TUN)

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2024-07-08

Some applications of Bratu integral equations in science and their numerical solutions

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Citation

M. GUECHI Somia, (2024-07-08), "Some applications of Bratu integral equations in science and their numerical solutions", [international] 2ème Conférence Internationale sur les Sciences Appliquées et l'Innovation (CISAI-2024) , sousse, Tunisie, Tunisia

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2024-04-28

Numerical Solution of Volterra-Hammerstein Integral Equation of the First Kind by Finite Difference Method Decomposition with Nyström Method

According to common knowledge, the first kind of Volterra integral equation is an
example of a problem that is not well-posed. This kind of equation is encountered in
several problems of science, and it is useful in a variety of fields, including control
theory, nuclear reactors, and ecological systems, where it can be used to evolutionary
processes. In this article, we'll present an effective and accurate technique to converting
VK1 into those of the second kind (VK2) and the kernel must not be zero for the
conversion process to be effective, and we will find the approximation solutions of them
by using the decomposition of Taylor series with Nyström method (Trapezoidal and
Simpson’s rules). In finality, we will present a variety of numerical examples to
demonstrate that the conversion that has been proposed is both successful and stable.
Citation

M. GUECHI Somia, (2024-04-28), "Numerical Solution of Volterra-Hammerstein Integral Equation of the First Kind by Finite Difference Method Decomposition with Nyström Method", [national] Mathematical Modeling of Engineering Problems , Mathematical Modeling of Engineering Problems

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2023-12-13

Inteegral equations and their applications in biological laboratoires and solve a chemical reactor problem

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Citation

M. GUECHI Somia, (2023-12-13), "Inteegral equations and their applications in biological laboratoires and solve a chemical reactor problem", [national] La 2ème Roncontre”Modélisation Mathématiques pour la Biologie et la Santé” , M'sila, Algeria

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2023-04-28

Effective Technique for Converting Ill-Posed Volterra Equation to Integro-Differential Equation and Solving It

The different types of integral equations are very important in practice life. Volterra integral equations of the first kind are not a lower interest them, then the study of the values of the solutions and methods for solving these equations with continuous kernels is a must be a step. However, it is well known that these equations are ill- posed problems. Therefore, in this paper, we will provide a new technique for finding solutions to these problems, by using conversion these integral equations of the first kind to integro-differential equations of the second kind using Taylor series. In this article, we apply this technique with some numerical methods such as modified Simpson method and finite difference method. Finally, we will present four numerical examples that demonstrate the performance and efficiency of our technique.
Citation

M. GUECHI Somia, (2023-04-28), "Effective Technique for Converting Ill-Posed Volterra Equation to Integro-Differential Equation and Solving It", [international] Mathematical Modelling of Engineering Problems , Mathematical Modelling

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2018-01-24

Numerical methods to solve nonlinear integral equations Numerical methods to solve nonlinear integral equations

Many problems which arise in mathematical physics, engineering, biology, economics,…etc., lead to mathematical models described by nonlinear integral equations. The aim of this research is to find the solution of nonlinear Volterra and Fredholm integral equation by using analytical and numerical methods such as the degenerate kernel method, the successive approximation method, the projection method, and the Nyström method. Also, we applied the new combination of Newton-Kantorovich method with modified Simpson method. Most of them transform the nonlinear integral equation into a system of linear or nonlinear algebraic equations. Finally, numerical examples are presented which demonstrate the robustness of the expansion numerical methods in determining solutions.
Citation

M. GUECHI Somia, (2018-01-24), "Numerical methods to solve nonlinear integral equations Numerical methods to solve nonlinear integral equations", [national] , LAP LAMBERT Academic Publishing (January 24, 2018)

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2017-10-09

TAYLOR SERIES FOR SOLVING LINEAR AND HAMMERSTEIN ILL-POSED VOLTERRA PROBLEMS VIA ITERATIONS METHOD

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Citation

M. GUECHI Somia, (2017-10-09), "TAYLOR SERIES FOR SOLVING LINEAR AND HAMMERSTEIN ILL-POSED VOLTERRA PROBLEMS VIA ITERATIONS METHOD", [international] The first international conference on the evolution of contemporary mathematics and their impact in science and technology (ECMI-SciTech), 09-12 October, Constantine, Algeria, 2017 , Constantine, Algeria

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2016-06-06

The combination of modified Simpson and Newton-Kantrovich methods for solving nonlinear integral equations

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Citation

M. GUECHI Somia, (2016-06-06), "The combination of modified Simpson and Newton-Kantrovich methods for solving nonlinear integral equations", [national] Advanced studies in contemporary mathematics. , Advanced studies in contemporary mathematics.

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