A numerical regime for 1-D Burgers’ equation using UAT tension B-spline differential quadrature method

Abstract

Present work deals with the numerical solution of 1D nonlinear Burgers’ equation. In this article, modified cubic uniform algebraic trigonometric tension B-spline is implemented as the basis function. Modified cubic UAT tension B-spline is incorporated in the differential quadrature method to fetch the values of weighting coefficients, as finding the weighting coefficients is the main key in differential quadrature method. After the spatial discretization of the equations, the reduced system of ordinary differential equations is obtained, which is tackled by employing the SSP-RK43 scheme. Accuracy of the present regime is verified by implementing notion of $L_{\infty }$ and $L_2$ error norms. On making comparisons with the earlier outcomes, it is noticed that present regime has produced better results, as well as is easy to implement. Main outcome of this work lies in findings of the better numerical approximations of some linear and nonlinear partial differential equations, specifically where the analytical solutions do not exist.

Keywords:

• 1D Burgers’ equation
• uniform algebraic trigonometric (UAT) tension B-spline
• strong stability-preserving Runge-Kutta 43 (SSP-RK43) scheme
• differential quadrature method (DQM)

Disclosure statement

No potential conflict of interest was reported by the authors.