Study of dynamical behavior of Burgers' equation in quantum modeling

Abstract

Our main goal is to investigate the dynamical behavior of the quantum model of Bateman–Burgers equation utilizing a new hybrid semidiscretization technique: nCB‐DQT‐RK scheme. The nCB‐DQT‐RK is traditional differential quadrature technique (DQT) with newly modified cubic B‐splines (nCB), as a basis, which have been utilized for the discretization of spatial derivatives, and the time integration scheme SSP‐RK for the temporal discretization. The efficiency/effectiveness of the reported nCB‐DQT‐RK results, computationally, are illustrated not only numerically but also graphically for better cognizance and reliable performance of the nCB‐DQT‐RK. This is validated based on the estimation of evaluated accuracy by means of stability and convergence analysis, which infer that the proposed nCB‐DQT‐RK scheme is capable of producing stable results with spatial convergence of order four, and the use of nCB in DQT is capable to improve performance (in terms of accuracy and spatial rate of convergence as well) as compared to existing techniques (collocation/quadrature) with traditional cubic B‐splines and its existing modifications, and so, nCB is capable to surpass cubic B‐splines and its existing modification.