PhD Computational Mathematics Candidate, Reduced-Order Modeling

Atif Ali Zafar

Passport: EG******* Date of birth: 1995/07/24 Place of birth: Rawalpindi, Pakistan

Nationality: Pakistani Phone number: +92-331******* (Mobile) Email address: *************@*****.*** Email address: ************@*****.*** https://orcid.org/: https://orcid.org/0009-0008-4428-278X

Address: H/No: 693, St 22, Sec 03, Samarzar Colony Adyala Road, District- Rawalpindi, 46000, Rawalpindi, Pakistan (Home)

I have a strong talent and deep interest in solving problems. Whether it is finding solutions to complex theoretical challenges or addressing real-world problems, I am always excited by the process and engage in it with great enthusiasm. Mathematics, particularly applied mathematics, fascinates me deeply, and I aspire to pursue a PhD in Applied Mathematics. Through my academic journey and research, I aim to contribute meaningfully to society and become a valuable asset by applying mathematical knowledge to solve practical problems. 2020/09/02 – 2023/09/08 Islamabad, Pakistan

MASTER OF PHILOSOPHY IN MATHEMATICS Capital University of Science and Technology Address Islamabad Expressway, Kahuta Road Zone-V Sihala, Islamabad, Pakistan Website https://cust.edu.pk/ Field of study Mathematics Final grade 3.50/4

2021/03/10 – 2022/08/05 Pakistan

BACHELOR OF EDUCATION (B.ED 1.5 YEAR) Allama Iqbal Open University Islamabad Address Sector H-8, Islamabad, Pakistan Website https://www.aiou.edu.pk/ Field of study Teacher training with subject specialisation, Training for pre-school teachers Final grade A 2016/09/01 – 2020/06/02 Pakistan

BACHELOR OF SCIENCE IN MATHEMATICS International Islamic University Islamabad Address H-10, Islamabad, 44000, Pakistan Website https://www.iiu.edu.pk/ Field of study Mathematics (Pure and Applied Courses) Final grade 3.52/4 2015/08/15 – 2016/07/10 Pakistan

HSSC-II Fauji Foundation College for Boys, New Lalazar Address New Lalazar, Rawalpindi, 44000, Pakistan

2014/08/15 – 2015/07/15 Pakistan

HSSC-I 502 Model College, Lalazar

Address Lalazar, Tulsa Road, Adiala Road, Lalazar, Rawalpindi, 46000, Pakistan 2011/08/15 – 2013/07/15 Pakistan

MATRICULATION CERTIFICATE (SSC-I AND SSC-II) Army Public School and College for Boys, Ordnance Road Address Khadim Hussain Rd, Lalkurti, Rawalpindi, 46000, Pakistan RESEARCH ANALYST – IDEAL SOLUTIONS SMC-PRIVATE LIMITED – 2022/11/30 – Current – ISLAMABAD, PAKISTAN ABOUT ME

EDUCATION AND TRAINING

WORK EXPERIENCE

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Leveraging MPhil in Mathematics to drive data-driven research, analysis, and strategic insights to support software development and business operations.

Key Responsibilities:

• Conduct research to support software development and business operations.

• Perform data analysis and interpretation for diverse projects.

• Evaluate project requirements and provide actionable insights.

• Prepare analytical reports, documentation, and research materials for multiple initiatives.

• Contribute to solution design and process improvement initiatives.

• Collaborate with developers, QA teams, and project managers to enhance decision-making.

• Assist in developing analytical frameworks for ongoing projects.

• Ensure high-quality, consistent work output across all tasks.

• Apply logical decision-making and structured analysis to solve complex problems. Key Skills and Expertise:

• Data-driven research and analysis

• Analytical reporting and documentation

• Problem-solving and structured decision-making

• Cross-functional collaboration and teamwork

• Process improvement and solution design

FREELANCING RESEARCH PAID PROJECT – NUST SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

(NUST-SEECS) ISLAMABAD, PAKISTAN – 2025/08/10 – 2025/11/15 – ISLAMABAD, PAKISTAN FREELANCING RESEARCH PAID PROJECT – DEPARTMENT OF MATHEMATICS, NATIONAL UNIVERSITY OF MODERN LANGUAGES, ISLAMABAD, PAKISTAN – 2024/08/15 – 2025/09/10 – ISLAMABAD, PAKISTAN INDEPENDENT RESEARCHER IN APPLIED MATHEMATICS (COLLABORATING WITH ACADEMIC FACULTY) – CAPITAL UNIVERSITY OF SCIENCE AND TECHNOLOGY – 2022/11/30 – Current – ISLAMABAD, PAKISTAN I have a strong research interest in applied mathematics and fluid mechanics, with particular emphasis on computational and non-Newtonian fluid dynamics. After completing my MPhil, I continued working as an independent researcher on the mathematical modeling and numerical simulation of complex fluid flows, incorporating various physical effects and geometrical configurations. Through a PhD, I aim to strengthen my expertise in advanced numerical and analytical–computational methods and collaborate internationally in computational fluid dynamics.

Numerical and Analytical Techniques Employed

1. Finite Difference Method (FDM)

The Finite Difference Method (FDM) is extensively used in my research to solve differential equations arising from fluid flow models by discretizing the computational domain and approximating derivatives. Both explicit and implicit schemes, including the Keller Box Method, are implemented to ensure numerical stability and accuracy. MATLAB and MAPLE are used to compute and analyze velocity, temperature, and concentration profiles. 2. Shooting Method (Using MATLAB bvp4c)

For boundary value problems obtained through similarity transformations, the Shooting Method is used to convert them into equivalent initial value problems. Numerical integration is performed using Runge–Kutta schemes, coupled with Newton’s method to satisfy boundary conditions. MATLAB’s bvp4c solver is extensively employed due to its high accuracy and adaptive mesh refinement, and it serves as a reliable tool for validating results. 3. Finite Element Method (FEM)

The Finite Element Method (FEM) is employed for problems involving complex geometries and boundary conditions, where FDM becomes less effective. I utilize FEM-based software such as COMSOL Multiphysics and FreeFEM++ for simulations, while ParaView and Tecplot are used for post-processing and visualization. Numerical results are systematically organized and presented using MS Excel and MS PowerPoint for clear graphical interpretation and comparative analysis.

4. Homotopy Analysis Method (HAM)

The Homotopy Analysis Method (HAM) is a powerful semi-analytical technique for solving strongly nonlinear differential equations without requiring small or large perturbation parameters. One of its key advantages is the ability to control solution convergence, which ensures accurate and reliable series solutions. MATLAB and Mathematica are used to construct solutions, analyze convergence behavior, and validate numerical results. 5. Simplified Finite Difference Method (SFDM)

The Simplified Finite Difference Method (SFDM) is implemented in MATLAB to reduce computational complexity while maintaining acceptable numerical accuracy. This approach is particularly effective for parametric and sensitivity studies, allowing rapid simulations of nonlinear fluid flow models. 6. Statistical Analysis

(Response Surface Methodology and Sensitivity Analysis) 2 / 6

To investigate the influence of key physical parameters, Response Surface Methodology (RSM) and Sensitivity Analysis are employed. Numerical response data are extracted from MATLAB simulations, while Minitab is used for statistical modeling, regression analysis, and optimization. This integrated approach helps identify dominant parameters, interaction effects, and optimal operating conditions, thereby enhancing the validation and robustness of numerical findings.

7. Artificial Neural Networks (ANN)

Artificial Neural Networks (ANN) are developed in MATLAB to construct data-driven predictive models based on numerical simulation datasets. ANN techniques are used to approximate complex nonlinear relationships between input parameters and output responses, significantly reducing computational cost and enabling rapid prediction for complex fluid flow systems.

8. Regular Perturbation Method

The Regular Perturbation Method is applied using Mathematica to obtain approximate analytical solutions for problems with small perturbation parameters, providing valuable physical insight. TEACHING PRACTICE EXPERIENCE (B.ED) – GOVT. HIGH SCHOOL DHOONG TEHSIL GUJAR KHAN DISTRICT – 2021/11/30 – 2022/11/30 – RAWALPINDI, PAKISTAN

During my B.Ed teaching practice, I worked as a Mathematics Lecturer at Govt. High School Dhoong, Tehsil Gujar Khan. This experience provided me with practical exposure to classroom teaching and helped me develop effective instructional and communication skills. I learned how to teach mathematics in an engaging way while making use of modern teaching techniques and technology.

Key Learning Outcomes and Responsibilities:

• Delivered mathematics lectures to students of different classes.

• Prepared lesson plans according to the curriculum and students’ learning needs.

• Applied effective teaching strategies to explain concepts clearly and simply.

• Used educational technology, including visual aids and multimedia tools, to enhance learning.

• Managed classroom activities and maintained a positive learning environment.

• Improved communication skills, confidence, and student interaction techniques. SENIOR MATH TEACHER – ALLIED SCHOOL GULSHANABAD CAMPUS – 2020/11/30 – 2021/11/30 – RAWALPINDI, PAKISTAN As a Senior Mathematics Teacher at Allied School, Gulshanabad Campus, I was responsible for delivering high- quality mathematics instruction to both middle and high school students. My role focused on fostering strong conceptual understanding, improving problem-solving skills, and ensuring academic success across all grade levels. Key Responsibilities and Achievements:

• Taught middle and high school mathematics courses, emphasizing both theoretical concepts and practical problem-solving.

• Developed comprehensive unit plans, lesson plans, and instructional materials tailored to student learning needs.

• Maintained accurate and up-to-date student records in compliance with school policies, district regulations, and legal requirements.

• Implemented teaching strategies that enhanced student engagement, understanding, and performance across the school network.

SCIENCE TEACHER – ALLIED SCHOOL NEW LALAZAR CAMPUS – 2019/11/30 – 2020/11/30 – RAWALPINDI, PAKISTAN As a Science Teacher at Allied School, New Lalazar Campus, I was responsible for delivering structured and engaging science lessons while fostering students’ curiosity and understanding of scientific concepts. My role focused on providing meaningful learning experiences and supporting students’ academic and personal development. Key Responsibilities and Achievements:

• Established and communicated clear objectives for all learning activities.

• Planned and implemented appropriate and engaging learning experiences tailored to student needs.

• Monitored, observed, and evaluated students’ performance and development regularly.

• Maintained accurate and comprehensive records of students’ progress and achievements.

• Encouraged a positive learning environment to enhance student participation and understanding. MATLAB Win Edt 10 Tex Studio for Books/Thesis/Manuscript MS Office(MS Word,MS Powerpoint,MS Excel,MS) Overleaf LaTex editor Comsol Multyphysics Paraview (basic) Free FEM++ Notepad/Notepad++ Visual studio/ visual studio code Mathematica Wolfram Maplesoft MINITAB software Design Expert (design of experiments) Fortran 90

SKILLS

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Mother tongue(s): URDU

Other language(s):

UNDERSTANDING SPEAKING WRITING

Listening Reading Spoken production Spoken interaction ENGLISH B2 C1 B1 B1 B2

Levels: A1 and A2: Basic user; B1 and B2: Independent user; C1 and C2: Proficient user Master Thesis

Title: Unsteady 3D Powell-Eyring Flow of Copper and Silicon-Carbide/Methanol for a Boundary Layer Using Cattaneo- Christov Model with Entropy Analysis.

Supervisor: Prof. Dr. Muhammad Sagheer (https://cust.edu.pk/our_team/dr-muhammad-sagheer-2/) Link https://thesis.cust.edu.pk/

Publication Section

1) Description:

Position: 1st Author (out of 4 Authors) and Corresponding Author Journal Name: PU-Punjab University Journal of Mathematics Journal Category: Emerging Sources Citation Index (ESCI) Status: Published Online

Link: Zafar, Atif Ali, et al. “Modeling Micromagnetorotational Dynamics in Magneto-Micropolar Fluids with Thermal Relaxation Effects.” Punjab University Journal of Mathematics, Dec. 2025, p. 757, https://doi.org/10.52280/pujm. 2025.57(07)04.

2) Description:

Position: 1st Author (out of 3 Authors) and Corresponding Author Journal Name: Computational Methods for Differential Equations Journal Category: Emerging Sources Citation Index (ESCI) Status: Published Online

Title: Numerical Simulations of Tangent Hyperbolic Fluid Flow is Performed on the Upper Horizontal Surface of a Paraboloid of Revolution by Keller Box Method

3) Description:

Position: 1st Author (out of 3 Authors)

Journal Name: Chemical Product and Process Modeling Journal Category: Emerging Sources Citation Index (ESCI) Status: Published Online

Title: Irreversibility Analysis of Unsteady Three-Dimensional Powell-Eyring Flow of Nanofluids in a Non-Fourier Model 4) Description:

Position: 1st Author (out of 2 Authors) and Corresponding Author Journal Name: Computational Methods for Differential Equations Journal Category: Emerging Sources Citation Index (ESCI) Status: Revision Process

Title: Comparative Numerical Analysis of Shooting Method and bvp4c for Unsteady MHD 3D Powell–Eyring Nanofluid Flow over a Bidirectionally Stretching Surface

5) Description:

Position: 1st Author (out of 3 Authors) and Corresponding Author Journal Name: International Journal of Numerical Methods for Heat & Fluid Flow Journal Category: Science Citation Index Expanded (SCIE) Status: Submitted for Publication

Title: Numerical Investigation of Jeffery–Hamel Flow and Heat Transfer of a Third-Grade Ternary Hybrid Nanofluid in Convergent–Divergent Channels with Stretching/Shrinking Walls: A Keller-Box Approach LANGUAGE SKILLS

PROJECTS

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2023/01/14 Capital University of Science and Technology, Islamabad, Pakistan Certificate of Participation–CUST Conference on Mathematics 2023 Talks:

Dr. Muhammad Sabeel Khan: “On the Generalized Continuum Theories and Materials Simulations”

Prof. Dr. Azad Akhtar Siddiqui: “Generating Approximate Closed-Form Solutions of Partial differential Equations”

Dr. Azhar Hussain: “Existence and Uniqueness of Solutions for q-Fractional Boundary Value Problems”

Prof. Dr. Liaqat Ali Khan: “Non-standard Analysis”

Prof. Dr. Asghar Qadir: “A Talk on the Importance of Basic Sciences” Link https://cust.edu.pk/

2024/01/31

English Proficiency Certificate – Capital University of Science and Technology, Islamabad, Pakistan 2021/11/30

Certificate of Outstanding Performance in Bachelor of Education (B.Ed) Workshop – Allama Iqbal Open University, Islamabad, Pakistan

2020/11/30

Dean’s Honor Roll – Capital University of Science and Technology, Islamabad, Pakistan 2019/11/30

English Proficiency Certificate – International Islamic University, Islamabad, Pakistan 2016/11/30

Certificate of Participation - Chess Championship – International Islamic University, Islamabad, Pakistan

2016/11/30

Financial Assistance Scholarship – International Islamic University, Islamabad, Pakistan 2016/11/30

National Prime Minister Laptop Scheme – Higher Education Commission (HEC), Pakistan Computational Tools

C: Intermediate, C++: Intermediate, HTML: Basic

Communicatios Skills:

I have strong communication and presentation skills, with effective leadership, coaching, and teamwork abilities.

Dr. Shafqat Hussain

Position: Professor

Email: *******.*******@****.**-********.**

Tel: +92-300-*******

Dr. Muhammad Sagheer

Position: Professor / HOD Mathematics

Email: *******@****.***.**

CONFERENCES AND SEMINARS

HONOURS AND AWARDS

LANGUAGES

SOFT SKILLS AND STRENGTHS

RECOMMENDATIONS

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Tel: +92-332-*******

Dr. Rashid Ali

Position: Professor

Email: ******.***@****.***.**

Tel: +92-332-*******.

Dr. Dur e Shehwar

Position: Professor

Email: *.*.*******@****.***.**

Tel: +92-332-*******

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