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Hire Ogugua N O.

United States

USD 55 /hr

Applied Mathematician | Nonlinear PDE Validation & Reaction–Diffusion Modeling (MATLAB, Maple)

Profile Summary

I am an applied mathematician specializing in the validation and semi-analytical benchmarking of nonlinear partial differential equation (PDE) models, with particular emphasis on reaction–diffusion systems arising in biology, chemistry, and engineering applications. Many nonlinear PDE models do not admit closed-form exact solutions, which makes it challenging to assess whether numerical simulations are convergent, stable, and physically reliable—especially at intermediate and late times where nonlinear effects dominate. My work focuses on addressing this gap by constructing independent semi-analytical reference solutions using the Homotopy Analysis Method (HAM) and systematically comparing them against numerical solvers implemented in MATLAB and Maple. In a recent validation study of a nonlinear Fisher reaction–diffusion model, I developed a time–power series HAM approximation, calibrated its convergence using an ℎ h-curve strategy, and benchmarked the resulting series against a high-resolution MATLAB pdepe solution. This approach provided strong early- and mid-time agreement while transparently identifying truncation limits at later times—exactly the type of diagnostic insight needed to build confidence in nonlinear simulations when no exact solution exists. I support clients through short, focused consulting engagements that include: - semi-analytical validation of nonlinear PDE models, - reaction–diffusion model benchmarking, - independent verification of numerical solvers, - convergence and truncation analysis for series-based methods, and - delivery of clear, reproducible technical reports with code and plots. My work is particularly well-suited for projects requiring independent mathematical verification before publication, parameter studies, or further model development. I value clarity, reproducibility, and transparent error analysis, and I tailor each engagement to the specific structure and goals of the client’s model.

Subject Matter Expertise

• ☆ Applied Mathematics
• ☆ Mathematical Models
• ☆ Mathematical Physics
• ☆ Differential Equations
• ☆ Computational Mathematics
• ☆ Mathematical Logic

Services

• Research

Research User Research, Fact Checking, Scientific and Technical Research

Work Experience

Associate Professor

Indian River State College

- Present

Associate Professor w/ Tenure

Indian River State College

January 2015 - Present

Instructor

Florida Institute of Technology

January 2006 - December 2011

Education

PhD (Mathematics)

Florida Institute of Technology

- Present

Doctor of Philosophy

Florida Institute of Technology

January 2008 - December 2012

Certifications

• Certification details not provided.

Publications

JOURNAL ARTICLE

Ogugua N. Onyejekwe (2025). An Inverse Problem for A Time-Fractional Heat Equation: De‎termination of A Time-Dependent Coefficient Via The Laplace ‎Homotopy Analysis Method . International Journal of Applied Mathematical Research.

Ogugua N. Onyejekwe (2025). Homotopy Analysis Method Solution to Time-Fractional Diffusion with a Moving Boundary . Journal of Applied Mathematics and Physics.

Ogugua Onyejekwe A Semi-Analytical Solution of a Two-Dimensional Moving Boundary Problem Using the Homotopy Analysis Method . Semarak International Journal Of Fundamental And Applied Mathematics.