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Ahlberg, J.H., Nilson, E.N. and Walsh, J.L. (1967) The Theory of Splines and Their Applications. Mathematics in Science and Engineering: A Series of Monographs and Textbooks. 1st Edition, Academic Press, Cambridge, MA.

has been cited by the following article:

• TITLE: Quintic B-Spline Method for Solving Sharma Tasso Oliver Equation

  AUTHORS: Talaat S. Eldanaf, Mohamed Elsayed, Mahmoud A. Eissa, Faisal Ezz-Eldeen Abd Alaal

  KEYWORDS: Nonlinear Partial Differential Equations, Sharma-Tasso-Olver (STO) Equation, Quintic B-Spline Collocation Method, Von Neumann Stability Analysis

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.12, December 30, 2022

  ABSTRACT: When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The quintic B-spline collocation method is used for solving such nonlinear partial differential equations. The developed plan uses the collocation approach and finite difference method to solve the problem under consideration. The given problem is discretized in both time and space directions. Forward difference formula is used for temporal discretization. Collocation method is used for spatial discretization. Additionally, by using Von Neumann stability analysis, it is demonstrated that the devised scheme is stable and convergent with regard to time. Examining two analytical approaches to show the effectiveness and performance of our approximate solution.