PhD Computational Mathematics Candidate

Mohamed Hussein Mohamed Salama

Mohamed H. Salama (publication name) Assistant Lecturer in Mathematics Department of Mathematics, Faculty of Science, Kafrelsheikh University, Egypt **********@*****.*** *******.************@***.***.***.**

+20-109-***-**** ORCID: 0009-0007-7248-6459

Academic Profile

Assistant Lecturer in Mathematics with an M.Sc. in Numerical Analysis and a research record in computational meth- ods for differential equations, structured discretisation, and numerical verification. Coauthor of seven peer-reviewed journal publications (five first-author). Interested in extending this foundation towards reduced-order modelling, sim- ulation of time-dependent systems, and physics–data-informed scientific computing. Education

M.Sc. in Mathematics (Numerical Analysis) 2023–2026 Kafrelsheikh University, Egypt

Thesis: “Spectral Solutions of Some Boundary and Initial Value Problems via Some Special Polynomials.” Defended 13 June 2026; University Council degree approval 28 July 2026. Preliminary coursework: 84.2% (Very Good); ranked first in the department in the preliminary-coursework year. B.Sc. in Mathematics 2017–2021

Kafrelsheikh University, Egypt

Excellent with Honors; cumulative result 90.3% (institutional GPA 4.03/5.00). Ranked first in the Department of Math- ematics; Top Graduates Excellence Medal (2021).

Research Experience

• Numerical PDE formulations. Developed and investigated space–time Tau and tensor-product Galerkin formula- tions for the telegraph and two-dimensional Poisson equations, including matrix construction and numerical checks.

• Parameter-dependent differential systems. Studied coupled fractional Lanchester equations with time-dependent coefficients using spectral collocation; examined computed trajectories under different parameter choices.

• Computational verification. Examined approximation errors, residuals, conditioning and convergence behaviour; compared numerical results with exact, reference or published solutions.

• Interdisciplinary collaboration. Coauthored a review integrating quantitative and physicochemical evidence in geo- science (Ore Geology Reviews, 2026).

Computational and Mathematical Skills

Numerical methods

Spectral collocation, Galerkin and Tau methods; ODEs, PDEs, fractional and integral equations; algebraic system formulation.

Verification

Numerical errors, residuals, conditioning, convergence studies, and comparisons with reference solutions.

Programming / tools

Mathematica for symbolic and numerical work; Python for numerical computation, parameter studies, visualisation and teaching (developing independent proficiency); LaTeX/Overleaf. Mathematical

foundation

Differential equations, numerical analysis, linear algebra, calculus, introductory dynamical sys- tems, probability and statistics.

Doctoral Research Interests

Numerical simulation of nonlinear and time-dependent systems; non-intrusive reduced-order modelling; parameter- dependent computation; physics–data-informed models; application-driven scientific computing, including fluid sys- tems.

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MOHAMED H. SALAMA ACADEMIC CURRICULUM VITAE

Peer-Reviewed Journal Publications (7)

NUMERICAL ANALYSIS AND COMPUTATIONAL MATHEMATICS 6 1. Y. H. Youssri, W. M. Abd-Elhameed, H. A. Zedan and M. H. Salama. “Spectral collocation treatment of neutral fractional panto- graph equations via shifted Lucas polynomials: analysis and implementation.” Ricerche di Matematica (online 2026). DOI. 2. M. H. Salama,H.A.Zedan,W.M.Abd-ElhameedandY.H.Youssri. “ASpectrallyAccurateShiftedLucasCollocationFramework for Fractional Lanchester Combat Dynamics with Time-Dependent Variable Coefficients.” Journal of Computational Applied Mechanics 57(3), 425–442 (2026). DOI.

3. M. H. Salama, H. A. Zedan, W. M. Abd-Elhameed and Y. H. Youssri. “Shifted Lucas Polynomial-Driven Tau Approach for the Telegraph Equation: Theoretical and Numerical Insights into Accuracy and Stability.” Computational and Applied Mathematics 45, Article 397 (2026). DOI.

4. M. H. Salama, R. M. Hafez, Y. H. Youssri, A. Alburaikan and H. A. E.-W. Khalifa. “Computational Error Analysis of Explicitly Defined Exponentially Fitted Szász–Mirakyan Operators.” Journal of Inequalities and Applications, Article 80 (2026). DOI. 5. M. H. Salama, H. A. Zedan,W.M. Abd-Elhameed andY.H. Youssri. “GalerkinMethodwithModifiedShiftedLucasPolynomials for Solving the 2D Poisson Equation.” Journal of Computational Applied Mechanics 56(4), 737–775 (2025). DOI. 6. M. H. Salama, H. A. Zedan, W. M. Abd-Elhameed and Y. H. Youssri. “Spectral Treatment of the Fractional Bratu Equation via Shifted Lucas Polynomials: A Precise Collocation Approach with Error Quantification.” Contemporary Mathematics 6(5), 6832–6870 (2025). DOI.

INTERDISCIPLINARY QUANTITATIVE REVIEW 1

7. A. S. Moftah, F. Wang, M. H. Salama, G. Tao and L. Zhang. “A unified magmatic-hydrothermal model for the IOA–IOCG continuum: Integrating geological, geochemical, quantitative, and physicochemical constraints.” Ore Geology Reviews, Article 107594 (online 13 October 2026; journal pre-proof). DOI. Review article. Academic Appointments

Assistant Lecturer in Mathematics Aug 2026–present Department of Mathematics, Kafrelsheikh University Teaching Assistant in Mathematics May 2022–Aug 2026 Department of Mathematics, Kafrelsheikh University Teaching Experience

Tutorials and teaching in numerical analysis, differential equations, calculus, linear algebra, probability and biostatistics. Introduced Python-basedmini-projects in numerical-analysis tutorials to connect algorithms with numerical experiments and visualisation.

Scholarly Activities

Research presentation “AnAccurateLucasCollocationFrameworkforFractionalLanchesterCombatDynamics,”Nile University, Egypt, 9 May 2026.

Peer reviewing Manuscript reviews in numerical analysis and differential equations. Languages

Arabic: Native. English: Used for the M.Sc. thesis, international journal publications and university teaching. Academic Referees

Prof. Youssri Hassan Youssri Prof. Waleed M. Abd-Elhameed Prof. Hassan Ahmed Zedan Cairo University, Egypt Cairo University, Egypt Kafrelsheikh University, Egypt *******@**.***.** ******@**.***.** ******.*****@***.***.***.** The three referees supervised the M.Sc. research and are research coauthors. 2 / 2

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