The Convergence of Geometric Mesh Cubic Spline Finite Difference Scheme for Nonlinear Higher Order Two-Point Boundary Value Problems. (23rd July 2014)

• Record Type: Journal Article
• Authors: Jha, Navnit; Mohanty, R. K.; Chauhan, Vinod
• Other Names: Dondi Riccardo Academic Editor.
• Is Part Of: International journal of computational mathematics. Volume 2014(2014)
• Publication Date: 2014-07-23
• Subjects: Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Periodicals; 518.05
• DOI: 10.1155/2014/527924
• Languages: English
• ISSNs: 2356-797X

Abstract

Abstract : An efficient algorithm for the numerical solution of higher (even) orders two-point nonlinear boundary value problems has been developed. The method is third order accurate and applicable to both singular and nonsingular cases. We have used cubic spline polynomial basis and geometric mesh finite difference technique for the generation of this new scheme. The irreducibility and monotone property of the iteration matrix have been established and the convergence analysis of the proposed method has been discussed. Some numerical experiments have been carried out to demonstrate the computational efficiency in terms of convergence order, maximum absolute errors, and root mean square errors. The numerical results justify the reliability and efficiency of the method in terms of both order and accuracy.