M. NADIR Mostefa

Prof

Directory of teachers

Department

Mathematics Department

Research Interests

Specialized in Mathematics Department. Focused on academic and scientific development.

Contact Info

University of M'Sila, Algeria

Email : mostefa.nadir@univ-msila.dz

On the Web:

  • Google Scholar N/A
  • ResearchGate
    ResearchGate N/A
  • ORCID N/A
  • SC
    Scopus N/A

Recent Publications

2025-04-06

Numerical solutions of Nonlinear Quadratic Volterra Integral Equations using Vieta-Lucas Wavelets

In this article, we present a numerical approach for solving Nonlinear Quadratic Volterra Integral Equations (NQVIEs) with the collocation method using Vieta-Lucas Wavelets (VLWs) and the Legendre Gauss Quadrature Rule (LGQR). First, we prove the existence and uniqueness of the main problem under specific conditions. Then, we apply the proposed method; the NQVIEs well be reduced to a system of nonlinear algebraic equations that can be solved by Newton’s method. We also estimate the error bound and the convergence of the presented method. Several numerical examples are mentioned in order to demonstrate its effectiveness and accuracy in solving NQVIEs.
Citation

M. NADIR Mostefa, (2025-04-06), "Numerical solutions of Nonlinear Quadratic Volterra Integral Equations using Vieta-Lucas Wavelets", [national] Applied Mathematics and Computational Mechanics , The Publishing Office of Czestochowa University of Technology

Read Full Paper
2021

Comparison between Taylor and perturbed method for Volterra integral equation of the first kind

As it is known the equation Aϕ = f with injective compact operator has a unique solution for all f in the range R(A).Unfortunately, the righthand side f is never known exactly, so we can take an approximate data fδ and used the perturbed problem αϕ + Aϕ = fδ where the solution ϕαδ depends continuously on the data fδ, and the bounded inverse operator (αI + A)−1 approximates the unbounded operator A−1 but not stable. In this work we obtain the convergence of the approximate solution of ϕαδ of the perturbed equation to the exact solution ϕ of initial equation provided α tends to zero with δ/√α.
.
Citation

M. NADIR Mostefa, (2021), "Comparison between Taylor and perturbed method for Volterra integral equation of the first kind", [national] Numerical Algebra, Control and Optimization , American Institute of Mathematical Sciences

Read Full Paper
2019

Quadratic numerical treatment for singular integral equations with logarithmic kernel

The goal of this paper is to present a direct method for an approximative solution of a weakly singular integral equations (WSIE) with logarithmic kernel on a piecewise smooth integration path using a modified quadratic spline approximation, we also show that this approximation gives an efficient approach to the analytical solution of WSIE.
Citation

M. NADIR Mostefa, (2019), "Quadratic numerical treatment for singular integral equations with logarithmic kernel", [national] Int. J. Computing Science and Mathematics , inderscience publishers

Read Full Paper
2014-10-28

UNE MÉTHODE NUMÉRIQUE DE RÉSOUDRE D' EQUITATION INTÉGRALES

Solving integral equations can be challenging in some cases; therefore, we resort to solving and processing them numerically. In this work, we will present a numerical solution based on the spectral method, approximating the solution using Legendre or Chebyshev polynomials.
Citation

M. NADIR Mostefa, (2014-10-28), "UNE MÉTHODE NUMÉRIQUE DE RÉSOUDRE D' EQUITATION INTÉGRALES", [national] CNEPA'14 , BORDJ BOU ARRÉRIDJ

Read Full Paper
2014

NUMERICAL SOLUTION OF HAMMERSTEIN INTEGRAL EQUATIONS IN Lp SPACES

In this work, we give conditions guarantee the boundedness of the Hammerstein integral operator in Lp spaces. The existence and the uniqueness of the solution of Hammerstein integral equation are treated under some ssumptions affected to the successive approximation, so that we obtain the convergence of the approximate solution to the exact one. Finally, we treat numerical examples to confirm our results.
Citation

M. NADIR Mostefa, (2014), "NUMERICAL SOLUTION OF HAMMERSTEIN INTEGRAL EQUATIONS IN Lp SPACES", [national] F A S C I C U L I M A T H E M A T I C I , Poznan University of Technology, Institute of Mathematics

Read Full Paper
2007

Two Points for the Adaptive Method for the Numerical Solution of Volterra Integral Equations

In this paper we add two points to the adaptive method for the numerical solution of Volterra integral equations of the second kind studied in [1]. We also present several numerical examples where we show the advantage of this method.
Citation

M. NADIR Mostefa, (2007), "Two Points for the Adaptive Method for the Numerical Solution of Volterra Integral Equations", [national] International Journal: Mathematical Manuscripts , Research India Publications

Read Full Paper
← Back to Researchers List