Open AccessExtended modified cubic B-spline algorithm for nonlinear Burgers' equation
Author(s) -
Mohammad Tamsir,
Neeraj Dhiman,
Vineet K. Srivastava
Publication year - 2016
Publication title -
beni-seuf university journal of basic and applied sciences /beni-suef university journal of basic and applied sciences
Language(s) - English
Resource type - Journals
eISSN - 2314-8543
pISSN - 2314-8535
DOI - 10.1016/j.bjbas.2016.09.001
Subject(s) - burgers' equation , nonlinear system , mathematics , quadrature (astronomy) , stability (learning theory) , runge–kutta methods , numerical analysis , b spline , algorithm , time stepping , monotone cubic interpolation , differential equation , mathematical analysis , computer science , discretization , physics , engineering , electrical engineering , quantum mechanics , machine learning , trilinear interpolation , linear interpolation , polynomial
In this paper, an extended modified cubic B-Spline differential quadrature method is proposed to approximate the solution of the nonlinear Burgers' equation. The proposed method is used in space and a five-stage and four order strong stability-preserving time-stepping Runge–Kutta (SSP-RK54) method is used in time. The accuracy and efficiency of the method is illustrated by considering four numerical problems. The numerical results of the method are compared with some existing methods and it was found that the proposed numerical method produces acceptable results and even more accurate results in comparison with some existing methods. The stability analysis of the scheme is also carried out and was found to be unconditionally stable