tailieunhanh - Nonpolynomial spline technique for the solution of ninth order boundary value problems

In this paper, a nonpolynomial spline technique is applied to solve the ninth order linear special case boundary value problems. The end conditions are derived to complete the definition of a spline. Three examples are numerically illustrated to check the efficiency of the method. | Turk J Math (2017) 41: 312 – 325 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article Nonpolynomial spline technique for the solution of ninth order boundary value problems Ghazala AKRAM∗, Zara NADEEM Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan Received: • Accepted/Published Online: • Final Version: Abstract: In this paper, a nonpolynomial spline technique is applied to solve the ninth order linear special case boundary value problems. The end conditions are derived to complete the definition of a spline. Three examples are numerically illustrated to check the efficiency of the method. The comparative analysis shows that the proposed technique gives better results than the homotopy perturbation method and the modified variational iteration method. Key words: Nonpolynomial spline, boundary value problems, end conditions, homotopy perturbation method, modified variational iteration method 1. Introduction Boundary value problems play an important role in various physical phenomena. Higher order boundary value problems have been considered due to their mathematical signification and strength in different fields of science. The depiction of ninth order boundary value problems exists rarely in the literature on numerical analysis. Mathematical modeling of AFTI-F16 fighters involves ninth order differential equations [4]. In view of the importance of the application of such problems in aircraft design and modeling, the present paper is devoted to the study of solutions of ninth order boundary value problems. Ninth order boundary value problems also arise in the study of astrophysics, hydrodynamics, and hydromagnetic stability [5, 6]. Siddiqi and Twizell [13–16] presented the solutions of 6th, 8th, 10th, and 12th order boundary value problems using sixth, eighth, tenth, and twelfth degree splines, .