A numerical scheme for solutions of a class of nonlinear differential equations. Issue 6 (1st November 2017)

• Record Type: Journal Article
• Authors: Yüzbaşı, Şuayip
• Is Part Of: Journal of Taibah University for science. Volume 11:Issue 6(2017)
• Page Start: 1165
• Page End: 1181
• Publication Date: 2017-11-01
• Subjects: Nonlinear differential equations -- Bessel functions of the first kind -- Collocation method -- Matrix method -- Numerical solutions; Science -- Periodicals; Science; Periodicals; 505
• DOI: 10.1016/j.jtusci.2017.03.001
• Languages: English
• ISSNs: 1658-3655

Abstract

Abstract: In this paper, a collocation method based on Bessel functions of the first kind is presented to compute the approximate solutions of a class of high-order nonlinear differential equations under the initial and boundary conditions. First, the matrix forms of the Bessel functions of the first kind and their derivatives are constructed. Second, by using these matrix forms, collocation points and the matrix operations, a nonlinear differential equation problem is converted to a system of nonlinear algebraic equations. The solutions of this system give the coefficients of the assumed approximate solution. To demonstrate the validity and applicability of the technique, numerical examples are included and comparisons are made with existing results. The results show the efficiency and accuracy of the present work.