Numerical solution of one-dimensional Burgers' equation by implementing the notion of Uniform Algebraic Hyperbolic (UAH) tension B-spline differential quadrature method

Abstract

In this paper, a novel approach "Uniform Algebraic Hyperbolic (UAH) tension B-spline Differential quadrature method" is implemented for the numerical approximation of 1D Burgers' equation. In this work, UAH tension B-spline basis function is used for the spatial discretization. After finding the weighting coefficients, the original system is reduced to the system of ordinary differential equations, when SSP-RK 43 scheme is implemented. Accuracy of the present method is tested by the means of $L_2$ and $L_\infty$ error norms. Present results are compared with existing results and these results are acceptable.