Quartic Non-Polynomial Spline for Solving the Third-Order Dispersive Partial Differential Equation
- 1 Department of Mathematics, College of Science and Arts, King Khalid University, Muhayil Asir, Saudia Arabia
- 2 Department of Mathematics, Faculty of Sciences and Arts, Taibah University, Medina, Saudi Arabia
- 3 Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt
- 4 Mathematics, College of Engineering & Science, Victoria University, Melbourne, Australia
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 analyt ical and approximate solution s is also shown for the illustrated example.
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