A numerical algorithm based on modified cubic trigonometric B-spline functions for computational modelling of hyperbolic-type wave equations. Issue 4 (12th June 2017)

• Record Type: Journal Article
• Authors: Alshomrani, Ali Saleh; Pandit, Sapna; Alzahrani, Abdullah K.; Alghamdi, Metib Said; Jiwari, Ram
• Is Part Of: Engineering computations. Volume 34:Issue 4(2017)
• Page Start: 1257
• Page End: 1276
• Publication Date: 2017-06-12
• Subjects: Stability -- Cubic trigonometric B-splines basis functions -- Hyperbolic-type wave equations -- SSP-RK54 scheme -- Thomas algorithm -- Modified cubic trigonometric B-splines basis functions; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-05-2016-0179
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: The main purpose of this work is the development of a numerical algorithm based on modified cubic trigonometric B-spline functions for computational modelling of hyperbolic-type wave equations. These types of equations describe a variety of physical models in the vibrations of structures, nonlinear optics, quantum field theory and solid-state physics, etc. Design/methodology/approach: Dirichlet boundary conditions cannot be handled easily by cubic trigonometric B-spline functions. Then, a modification is made in cubic trigonometric B-spline functions to handle the Dirichlet boundary conditions and a numerical algorithm is developed. The proposed algorithm reduced the hyperbolic-type wave equations into a system of first-order ordinary differential equations (ODEs) in time variable. Then, stability-preserving SSP-RK54 scheme and the Thomas algorithm are used to solve the obtained system. The stability of the algorithm is also discussed. Findings: A different technique based on modified cubic trigonometric B-spline functions is proposed which is quite different from the schemes developed (Abbas et al., 2014 ; Nazir et al., 2016 ) and depicts the computational modelling of hyperbolic-type wave equations. Originality/value: To the best of the authors' knowledge, this technique is novel for solving hyperbolic-type wave equations and the developed algorithm is free from quasi-linearization process and finite difference operators for time derivatives. This algorithm gives better results than the results discussed in literature (Dehghan and Shokri, 2008 ; Batiha et al., 2007 ; Mittal and Bhatia, 2013 ; Jiwari, 2015 ).