Payame Noor University (PNU) Control and Optimization in Applied Mathematics 2383-3130 11 2 2026 05 21 Computational Performance Optimization in Solving Singular Boundary Value Problems: A Comparative Study of Finite Difference and Collocation Methods 201 219 12800 10.30473/coam.2026.76880.1383 EN Saad Qasim Abbas Department of Medical Instruments Engineering Techniques, University of Bilad Alrafidain, Iraq Wasan Saad Ahmed Computer Science Department, University of Diyala, Iraq Journal Article 2025 12 19 This paper presents a systematic comparative study of two widely used numerical solvers --- HOFiD_bvp (high-order finite difference scheme) and bvp4c (collocation-based) --- for solving singular second-order ordinary differential equations (ODEs) with first-kind (regular) boundary singularities. Four representative benchmark problems drawn from fluid dynamics, materials science, and radially symmetric diffusion models are used to evaluate solver performance across key metrics: maximum residual, maximum error, mesh point count, and ODE/BC function call counts. Results show that HOFiD_bvp consistently achieves lower residuals and errors with fewer function evaluations, making it computationally more efficient. Conversely, bvp4c demonstrates superior robustness for nonlinear singular problems and offers better adaptive mesh refinement capabilities. These findings provide practical guidance for selecting the appropriate numerical technique in applied science and engineering contexts, with implications for optimization of computational simulation workflows. https://mathco.journals.pnu.ac.ir/article_12800_b93a6b280ee5f46dce6265d90f0d3b22.pdf