An Algorithm developed by implementing Modified Cubic Hyperbolic B-Spline based Differential Quadrature Method on non-linear Burgers’ equation

Abstract

Abstract Present paper proposed a novel regime has been proposed named “Modified Cubic Hyperbolic B-Spline Differential Quadrature Method.” In the present method, a cubic Hyperbolic B-spline is used as a test function in the “Differential quadrature method.” This method has been employed to test the effectiveness and feasibility of approximation of the 1-D Burgers’ equation. In order to check the compatibility of the proposed method, a variety of test problems are discussed. A comparison is made between L2 and L∞ error norms by considering some examples already present in literature. The corresponding set of Ordinary Differential Equations is solved by using the Strong-Stability-Preserving Runge-Kutta (43) method, i.e. (SSP-RK43) method. It has been observed that obtained results have excellent compatibility with numerical approximations discussed in literature. Stability of developed regime is addressed by eigen values method.”