Siraj-Ul-Islam, Khan, M.A., Tirmizi, I.A. and Twizell, E.H. (2005) Non-Polynomial Spline Approach to the Solution of a System of Third-Order Boundary-Value Problems. Applied Mathematics and Computation, 168, 152-163.
https://doi.org/10.1016/j.amc.2004.08.044

has been cited by the following article:

• 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.