A quartic trigonometric tension b-spline algorithm for nonlinear partial differential equation system. Issue 5 (26th October 2020)

• Record Type: Journal Article
• Authors: Ersoy Hepson, Özlem
• Is Part Of: Engineering computations. Volume 38:Issue 5(2021)
• Page Start: 2293
• Page End: 2311
• Publication Date: 2020-10-26
• Subjects: Numerical analysis -- Coupled burgers' equation -- Quartic trigonometric tension B-splines; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-05-2020-0289
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: The purpose of this study is to construct quartic trigonometric tension (QTT) B-spline collocation algorithms for the numerical solutions of the Coupled Burgers' equation. Design/methodology/approach: The finite elements method (FEM) is a numerical method for obtaining an approximate solution of partial differential equations (PDEs). The development of high-speed computers enables to development FEM to solve PDEs on both complex domain and complicated boundary conditions. It also provides higher-order approximation which consists of a vector of coefficients multiplied by a set of basis functions. FEM with the B-splines is efficient due both to giving a smaller system of algebraic equations that has lower computational complexity and providing higher-order continuous approximation depending on using the B-splines of high degree. Findings: The result of the test problems indicates the reliability of the method to get solutions to the CBE. QTT B-spline collocation approach has convergence order 3 in space and order 1 in time. So that nonpolynomial splines provide smooth solutions during the run of the program. Originality/value: There are few numerical methods build-up using the trigonometric tension spline for solving differential equations. The tension B-spline collocation method is used for finding the solution of Coupled Burgers' equation.