プロフィール詳細

プロジェクトを作成

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Ogugua N O.に依頼

United States

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

プロフィール概要

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.

専門分野

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

サービス

• Research

Research User Research, Fact Checking, Scientific and Technical Research

職務経験

Associate Professor

Indian River State College

- 現在

Associate Professor w/ Tenure

Indian River State College

1月 2015 - 現在

Instructor

Florida Institute of Technology

1月 2006 - 12月 2011

学歴

PhD (Mathematics)

Florida Institute of Technology

- 現在

Doctor of Philosophy

Florida Institute of Technology

1月 2008 - 12月 2012

認定資格

• 認定資格の詳細は未入力です。

出版物

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.