TITLE:
Quartic Non-Polynomial Spline for Solving the Third-Order Dispersive Partial Differential Equation
AUTHORS:
Zaki Mrzog Alaofi, Talaat Sayed Ali, Faisal Abd Alaal, Silvestru Sever Dragomir
KEYWORDS:
Non-Polynomial Spline, Third-Order Dispersive Partial Differential Equation, Stability, Convergent
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.11 No.3,
September
28,
2021
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.