Quartic Non-Polynomial Spline for Solving the Third-Order Dispersive Partial Differential Equation - American Journal of Computational Mathematics

AJCM > Vol.11 No.3, September 2021

American Journal of Computational Mathematics

Volume 11, Issue 3 (September 2021)

ISSN Print: 2161-1203 ISSN Online: 2161-1211

Google-based Impact Factor: 0.42 Citations

Quartic Non-Polynomial Spline for Solving the Third-Order Dispersive Partial Differential Equation ()

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Download as PDF (Size: 1692KB) PP. 189-206

DOI: 10.4236/ajcm.2021.113013 210 Downloads 992 Views Citations

Author(s)

Zaki Mrzog Alaofi^1,2, Talaat Sayed Ali³, Faisal Abd Alaal⁴, Silvestru Sever Dragomir²

Affiliation(s)

¹Department of Mathematics, College of Science and Arts, King Khalid University, Muhayil Asir, Saudia Arabia.
²Mathematics, College of Engineering & Science, Victoria University, Melbourne, Australia.
³Department of Mathematics, Faculty of Sciences and Arts, Taibah University, Medina, Saudi Arabia.
⁴Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt.

ABSTRACT

In the present paper, we introduce a non-polynomial quadratic spline method for solving third-order boundary value problems. Third-order singularly perturbed boundary value problems occur frequently in many areas of applied sciences such as solid mechanics, quantum mechanics, chemical reactor theory, Newtonian fluid mechanics, optimal control, convection-diffusion processes, hydrodynamics, aerodynamics, etc. These problems have various important applications in fluid dynamics. The procedure involves a reduction of a third-order partial differential equation to a first-order ordinary differential equation. Truncation errors are given. The unconditional stability of the method is analysed by the Von-Neumann stability analysis. The developed method is tested with an illustrated example, and the results are compared with other methods from the literature, which shows the applicability and feasibility of the presented method. Furthermore, a graphical comparison between analytical and approximate solutions is also shown for the illustrated example.

KEYWORDS

Non-Polynomial Spline, Third-Order Dispersive Partial Differential Equation, Stability, Convergent

Share and Cite:

Alaofi, Z. , Ali, T. , Alaal, F. and Dragomir, S. (2021) Quartic Non-Polynomial Spline for Solving the Third-Order Dispersive Partial Differential Equation. American Journal of Computational Mathematics, 11, 189-206. doi: 10.4236/ajcm.2021.113013.

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