Dr. Shams
Ul Arifeen

Assistant Professor · Applied Mathematics

Numerical methods for complex differential systems.

Explore research View publications

Mathematics
for a more predictable
tomorrow.

Dr. Shams Ul Arifeen
About

Rigorous computation,
useful understanding.

I am an Assistant Professor in the Department of Mathematics at the National University of Sciences & Technology, Islamabad. My work connects numerical analysis, approximation theory, and modern computational methods.

I completed my PhD in Applied Mathematics at Ghulam Ishaq Khan Institute of Engineering Sciences and Technology, where my thesis developed Galerkin and Petrov–Galerkin finite element methods for integer- and fractional-order differential equations.

Read curriculum vitae
Research

Computational mathematics
for systems in motion.

01

Numerical
computing

Reliable computational approaches for differential systems and scientific models.

02

Finite element
methods

Galerkin and Petrov–Galerkin techniques for integer and fractional equations.

03

Approximation &
machine learning

B-spline, polynomial, wavelet, and PINN-based approaches to direct and inverse problems.

Selected work

Publications

Research spanning fractional differential equations, B-spline methods, wavelet collocation, and numerical models.

  1. 2025

    Computational study of variable order time-fractional differential equations arising in modeling of transport processes and viscoelastic oscillator

    Ain Shams Engineering Journal, 16(9), 103532

  2. 2025

    Comparative study of slow and fast diffusion processes via quadratic and cubic B-spline Galerkin method

    Ain Shams Engineering Journal, 16(8), 103449

  3. 2025

    Numerical solution of seventh order KdV equations via quintic B-splines collocation method

    Alexandria Engineering Journal IF 6

  4. 2024

    Galerkin approximation of Burgers–Huxley equation with fractional order arising in reaction mechanism and diffusion transport

    Physica Scripta IF 2.6

  5. 2024

    Galerkin approximation for multi-term time-fractional differential equations

    Ain Shams Engineering Journal IF 6

  6. 2024

    Computational study of time-fractional non-linear Kawahara equations using quintic B-spline and Galerkin's method

    Partial Differential Equations in Applied Mathematics

  7. 2024

    Computational study of coupled Whitham Broer Kaup equations via interpolation technique

    Ain Shams Engineering Journal IF 6

  8. 2024

    Approximation of one and two dimensional nonlinear generalized Benjamin–Bona–Mahony Burgers' equation with local fractional derivative

    Computers and Mathematics with Applications IF 2.9

  9. 2024

    Numerical solution of third-order Rosenau–Hyman and Fornberg–Whitham equations via B-spline interpolation approach

    Axioms IF 1.9

  10. —

    Petrov–Galerkin approximation of time-fractional coupled Korteweg–de Vries equation for propagation of long wave in shallow water

    Mathematics and Computers in Simulation IF 3.601

  11. —

    Computational study of multiterm time-fractional differential equation using cubic B-spline finite element method

    Complexity IF 2.121

  12. —

    Numerical solutions of higher order boundary value problems via wavelet approach

    Advances in Difference Equations IF 2.830

  13. 2025

    Integrated Lucas and Fibonacci polynomial approach for time fractional fast and slow diffusion models

    International Journal of Modern Physics C IF 1.5

  14. 2024

    A hybrid kernel-based meshless method for numerical approximation of multidimensional Fisher's equation

    Mathematics and Computers in Simulation IF 4.6

  15. 2024

    On the analysis and application of a spectral collocation scheme for the nonlinear two-dimensional fractional diffusion equation

    Results in Physics IF 5.3

  16. —

    An efficient computational technique for higher order KdV equation arising in shallow water waves

    Applied Numerical Mathematics IF 2.994

  17. —

    A high-order reliable and efficient Haar wavelet collocation method for nonlinear problems with two point-integral boundary conditions

    Alexandria Engineering Journal IF 6.626

  18. —

    Approximate solution of second order singular perturbation and obstacle boundary value problems using meshless method based on radial basis functions

    Journal of Nonlinear Mathematical Physics IF 1.163

  19. —

    Numerical solutions of two dimensional Sobolev and generalized Benjamin–Bona–Mahony–Burgers equations via Haar wavelets

    Computers and Mathematics with Applications IF 3.128

  20. —

    Numerical study of 1D and 2D advection–diffusion–reaction equations using Lucas and Fibonacci polynomials

    Arabian Journal of Mathematics IF 3.128

Teaching

Teaching is where theory
becomes intuition.

Courses taught

  • Differential Geometry
  • Finite Volume Method
  • Numerical Computing
  • Calculus & Analytical Geometry
  • Multivariable Calculus
  • Linear Algebra
  • Probability & Statistics
  • Differential Equations

  1. Assistant Professor

    National University of Sciences & Technology, Islamabad

  2. Assistant Professor

    National University of Computer & Emerging Sciences, Peshawar

  3. Lecturer

    National University of Computer & Emerging Sciences, Peshawar

  4. Graduate Assistant

    Ghulam Ishaq Khan Institute of Engineering Sciences and Technology

  5. Visiting Lecturer

    Shuhada-e-Army Public School University of Technology, Nowshera

  6. Visiting Lecturer

    University of Swabi, Swabi

  7. Graduate Assistant

    Ghulam Ishaq Khan Institute of Engineering Sciences and Technology

Academic formation

A foundation in
applied mathematics.

PhD, Applied Mathematics

Ghulam Ishaq Khan Institute of Engineering Sciences and Technology

MS, Applied Mathematics

Ghulam Ishaq Khan Institute of Engineering Sciences and Technology

MS, Mathematics

University of Peshawar

Academic service & recognition

Tools, service, and
scholarly milestones.

Programming experience

  • MATLAB
  • Mathematica
  • Maple
  • Python
  • C

Journal peer review

  • International Journal of Applied and Computational Mathematics
  • Journal of Ocean Engineering and Science
  • Computers and Mathematics with Applications

Awards & scholarships

  • PhD Program Graduate Assistantship, Ghulam Ishaq Khan Institute of Engineering Sciences and Technology
  • MS Program Graduate Assistantship, Ghulam Ishaq Khan Institute of Engineering Sciences and Technology
  • MSc merit scholarship, Government of Khyber Pakhtunkhwa and Prime Minister fee reimbursement scheme
  • BSc merit scholarship, Hira Model School and Degree College, Drosh
  • Stoori da Khyber Pakhtunkhwa merit scholarship program

Conferences

  • International Photonics Symposium, Ghulam Ishaq Khan Institute of Engineering Sciences and Technology · April 2018
  • First International Pak–Turk Workshop on Emerging Technology in the Field of Science and Engineering · May 2018
  • Fourth Conference on Numerical Methods for Fractional-Derivative Problems
  • International Conference on Emerging Technologies, FAST-NUCES Peshawar Campus · 2023