A Spectral-Collocation and Spline-Based Numerical Framework for Solving Nonlinear Boundary Layer Flow Problems

Faraidun Hamasalh; Dr. shko Tahir; Balen Yassin

doi:10.69923/2detby27

A Spectral-Collocation and Spline-Based Numerical Framework for Solving Nonlinear Boundary Layer Flow Problems

Authors

Dr. Faraidun K. Hamasalh Sulaimani Polytechnic University Author https://orcid.org/0009-0000-8084-2440
Dr. shko Ali University of Sulaimani Author https://orcid.org/0000-0002-6780-7111
MSc Student Balen Yassin University of Sulaimani Author https://orcid.org/0009-0000-6444-301X

DOI:

https://doi.org/10.69923/2detby27

Keywords:

Spectral collocation, spline interpolation, polynomial interpolation, fluid dynamics.

Abstract

In this work we present a multi-step algorithm with high accuracy to solve nonlinear second- and third-order ODE problems in fluid dynamics. In this method we use the polynomial spectral collocation method to acquire accurate numerical values at the collocation points, followed by spline interpolation to improve the approximated solution between the collocation points. Also, we derived quintic and septic polynomial spline models and computed the associated error bounds with a convergence analysis. To demonstrate the application of the present method, we considered two cases of fluid dynamics problems. We also looked at the numerical solution's validity and convergence in each example, which are assessed by calculating the infinity norm of the absolute and residual errors at every iteration level. Lastly, we illustrate the effect and influence of the physical parameters over velocity and temperature profiles through graphical results.

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Author Biographies

Dr. Faraidun K. Hamasalh, Sulaimani Polytechnic University

I am Professor of Mathematics (Numerical Analysis), Sulaimani Polytechnic University, Department of Mathematics, College of Education, University of Sulaimani/ Sulaimani, Iraq. I was awarded PhD in Mathematics (Numerical Analysis) from Sulaimani University, Department of Mathematics, College of Science. My research interests include numerical solution of ODE, approximation by spline functions, Fluid Mechanics and Fractional Derivatives.

Now Dean of Bakrajo Technical Institute at Sulaimani Polytechnic University
Dr. shko Ali, University of Sulaimani

Department of Mathematics, College of Science, University of Sulaimani univsul.edu.iq üzerinde doğrulanmış e-posta adresine sahip - Ana Sayfa
MSc Student Balen Yassin, University of Sulaimani

Mr. Balen Dlshad YassinMSc Student in Applied Mathematics, Department of Mathematics, College of Education, University of Sulaimani.

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Published

09/30/2025

Issue

Vol. 2 No. 3 (2025): Volume 2, Issue 3

Section

Articles

License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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References

Marshall,G.C.and H.W.Ohm 1987 .Yield responses of 16 winter wheat cultivars to row spacing and seeding rate .Agronomy Journal .79:1027-1030

How to Cite

[1]

F. Hamasalh, D. shko Tahir, and B. Yassin, “A Spectral-Collocation and Spline-Based Numerical Framework for Solving Nonlinear Boundary Layer Flow Problems”, IJApSc, vol. 2, no. 3, pp. 35–47, Sep. 2025, doi: 10.69923/2detby27.